Explain how you would solve a triangles given two sides and the included angle?

Answers

Answer 1

Final answer:

To solve a triangle given two sides and included angle, use the law of cosines. This law is expressed as a² = b² + c² - 2bc cos(A), where a, b, c are the lengths of the sides, and A is the included angle.

Explanation:

To solve a triangle given two sides and the included angle, you would use the Law of Cosines. This law is used when you're given two sides and the included angle in a triangle (often abbreviated as SAS). The law states,

a² = b² + c² - 2bc cos(A)

where a, b, and c are the lengths of the sides of the triangle, and A is the included angle. So, in this case, if you're given sides b and c and included angle A, you would substitute these values into the formula to find side a.

For instance, if side b is 3 units, side c is 4 units, and angle A is 60 degrees, we would substitute these values into our formula like so: a² = 3² + 4² - 2(3)(4) cos(60).

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Answer 2

The correct way to solve a triangles given two sides and the included angle is by the sine and cosine rule.

Solving triangles using the sine and cosine rule

For angle placed in between two sides of a triangle, we can use the cosine rule to determine the unknown angle

According to the cosine formula, we will have:

[tex]a^2=b^2+c^2-2bc \ cos\theta[/tex]

where a, and c are the sides of the triangle and theta is the central angle.

Also, the remaining angles can be determined using the law of cosines as shown:
a/sinA = b/sinB = c/sinC

Hence the correct way to solve a triangles given two sides and the included angle is by the sine and cosine rule.

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Related Questions

At noon, ship a is 30 nautical miles due west of ship
b. ship a is sailing west at 23 knots and ship b is sailing north at 17 knots. how fast (in knots) is the distance between the ships changing at 4 pm?

Answers

Let the origin of the coordinate system be the position of ship B at noon. Then the distance between the ships as a function of t (in hours) is
.. d = √((30 +23t)² +(17t)²)
.. = √(818t² +1380t +900)

The rate of change of distance with respect to time is
.. d' = (1/2)(2*818*t +1380)/√(818t² +1380t +900)
.. = (818t +690)/√(818t² +1380t +900)

At t=4, this is
.. d' = (818*4 +690)/√(818*16 +1380*4 +900)
.. = 3962/√19508
.. ≈ 28.37 . . . . . knots

The distance between the ships is increasing at about 28.37 knots at 4 pm.

Final answer:

The rate at which the distance between the two ships is changing is approximately 18.86 knots at 4pm.

Explanation:

To find the rate at which the distance between the two ships is changing, we can use the concept of relative velocity. Let's consider ship A as the reference point. The velocity of ship A relative to the Earth is given as 23 knots due west, and the velocity of ship B relative to the Earth is given as 17 knots due north. The velocity of ship B relative to ship A can be found by subtracting the velocities.

Using the Pythagorean theorem, we can find the magnitude of the velocity of ship B relative to ship A. This magnitude represents the rate at which the distance between the ships is changing. Therefore, at 4 pm, the distance between the ships is changing at a rate of approximately 18.86 knots.

A stock had returns of 11 percent, -18 percent, -21 percent, 20 percent, and 34 percent over the past five years. what is the standard deviation of these returns?
a. 18.74 percent
b. 20.21 percent
c. 20.68 percent
d. 24.01 percent
e. 23.49 percent

Answers

Final answer:

The standard deviation of the returns is 21.5 percent.

Explanation:

To calculate the standard deviation of the returns, we need to follow these steps:

Calculate the mean of the returnsSubtract the mean from each return to find the deviationsSquare the deviationsCalculate the mean of the squared deviationsTake the square root of the mean of the squared deviations

Let's perform these steps:

The mean of the returns is (11 - 18 - 21 + 20 + 34) / 5 = 5.2 percentThe deviations are (11 - 5.2) = 5.8, (-18 - 5.2) = -23.2, (-21 - 5.2) = -26.2, (20 - 5.2) = 14.8, (34 - 5.2) = 28.8 percentThe squared deviations are 33.64, 538.24, 685.44, 219.04, 829.44 percent squaredThe mean of the squared deviations is (33.64 + 538.24 + 685.44 + 219.04 + 829.44) / 5 = 461.96 percent squaredThe square root of the mean of the squared deviations is sqrt(461.96) = 21.5 percent

Therefore, the standard deviation of the returns is 21.5 percent.

You are thinking about building a home. You are told that for a particular area, the construction costs for the home should be about four times the cost of the land and the landscaping costs should be about one-third of the cost of the land. If your total budget is $250,000, calculate your budget for the land.

Answers

land and land scaping with cost about 83k
250k-83k is 167k

construction : land : landscaping = 4 : 1 : 1/3 = 12 : 3 : 1
Then the land cost is expected to be 3/(12+3+1) = 3/16 of the total cost.

3/16 * 250,000 = 46,875

Your budget for the land should be about $46,875.

Can someone please help me with these questions I need them ASAP!

Answers

1.
a.Irrational
b. Irrational
c. Rational
d.Irrational

2.
Is Rational
Is an integer
Is a whole number

3.
Is Rational
Is a real number

4.
Is Rational

========================
As far as I can tell you got them all correct, well done :D

determine the values of x and y.
DEFG is a parallelogram.
DH = x + 3
HF = 3y
GH = 4x - 5
HE = 2y + 3
A) x = 2 and y = 3
B) x = 3 and y = 2
C) x = 3 and y = 6
D) x = 6 and y = 3

Answers

in parallelograms the diagonals bisect each other. this means that one diagonal cuts the other diagonal at its mid point.
GE cuts DF at H, then DH = HF
DH = x + 3
HF = 3y
Since DH = HF
x + 3 = 3y
3y - x = 3---->1)
GH = HE
4x - 5 = 2y + 3
4x - 2y = 3 + 5
4x - 2y = 8 ---> 2)
we have a set of simultaneous equations where we have to solve for x and y
3y - x = 3---->1)
4x - 2y = 8 ---> 2)
multiply 1st equation by 4
12y - 4x = 12 ---3)
add 2nd and 3rd equation
10 y = 20
y = 2
substitute y = 2 in 1st equation
3*2 - x = 3
6 - x = 3
x = 3 and y = 2
therefore correct response is B)

The walking distance from the Empire State Building in New York City to Times Square is about 9/10 mile. The walking distance from the Empire State Building into sues hotel is 8 times as far

Answers

The answer is 7 2/10 miles
what I did was multiply 9 and 8 to get 72/10 and turned the improper fraction into a mixed number to get 7 2/10

Answer: Walking distance is [tex]7\frac{2}{10}\ miles[/tex]

Step-by-step explanation:

Since we have given that

Walking distance from the Empire State Building in New York City to Times Square = [tex]\frac{9}{10}\ mile[/tex]

According to question, the walking distance from the Empire State Building into Sues Hotel is 8 times as far.

So, Walking distance from the Empire State Building into Sues Hotel is given by

[tex]8\times \frac{9}{10}\\\\=\frac{72}{10}\\\\=7\frac{2}{10}\ miles[/tex]

Hence, Walking distance is [tex]7\frac{2}{10}\ miles[/tex]

6 students share 4 bagels equally. How many pieces does each person get? (p.s thanks to everyone who answers)

Answers

Hi!

You would get 1 and a half bagel for each person

6/4 = 1 1/2 or 1.5

Solution:

we are given that

6 students share 4 bagels equally.

we have been asked to find that

How many pieces does each person get?

Here we will have to use the concept of division. Because we are dividing bagels among the students.

So To get the number of pieces each will get divide 6 by 4.

Number of Pieces for each boys [tex] =\frac{6}{4}=\frac{3}{2}=1\frac{1}{2} \\ [/tex]

What is the total surface area of the figure shown

Answers

I think the answer is 3912.

Answer: The total surface area is 2784 sq. inches.

Step-by-step explanation: We are given to find the total surface area of the given figure.

Let us divide the figure into two two cuboids 1 and 2 as shown in the attached figure.

We know that the surface area of a cuboid with length 'l', breadth 'b' and height 'h' is given by

[tex]S.A.=2(l_1b_1+l_1h_1+h_1b_1).[/tex]

The dimensions of the cuboid 1 are

[tex]length,~l_1=14~\textup{inches},\\\\breadth,~b_1=12~\textup{inches},\\\\height,~h_1=24-10=14~\textup{inches}.[/tex]

The dimensions of the cuboid 2 are

[tex]length,~l_2=30~\textup{inches},\\\\breadth,~b_1=14~\textup{inches},\\\\height,~h_1=10~\textup{inches}.[/tex]

Therefore, surface area of cuboid 1 is given by

[tex]S.A_1\\\\=2(l_1b_1+l_1h_1+h_1b_1)\\\\=2(14\times 12+14\times 14+14\times 12)\\\\=2(532)\\\\=1064~\textup{sq. inches.}[/tex]

And surface area of cuboid 2 is given by

[tex]S.A_2\\\\=2(l_2b_2+l_2h_2+h_2b_2)\\\\=2(30\times 14+30\times 10+14\times 10)\\\\=2(420+300+140)\\\\=2(860)\\\\=1720~\textup{sq. inches}.[/tex]

Thus, the total surface area of the figure is

[tex]S.A.=S.A_1+S.A_2=1064+1720=2784~\textup{sq. inches}.[/tex]

A rectangular kitchen floor measures 18 feet by 15 feet. A stove on the floor has a rectangular base measuring 3 feet by 4 feet, and a refrigerator covers a rectangular area of the floor measuring 4 feet by 5 feet. How many square feet of tile will be needed to cover the kitchen floor not counting the area used by the stove and the refrigerator?

Answers

Stove area = 12 square feet
Refrigerator area = 20 square feet
Entire kitchen floor = 270 square feet
12 + 20 = 32 square feet
270 square feet - 32 square feet = 238 square feet
238 square feet will be needed

Number of square feet of tile will be needed to cover the kitchen floor is 238 square feet.

Given that, a rectangular kitchen floor measures 18 feet by 15 feet.

What is the area of a rectangle?

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Area of a rectangular kitchen floor

= 18×15

= 270 square feet

Area covered by a stove

= 3×4

= 12 square feet

Area covered by a refrigerator

= 4×5

= 20 square feet

Area covered by tiles

= 270-(12+20)

= 270-32

= 238 square feet

Therefore, number of square feet of tile will be needed to cover the kitchen floor is 238 square feet.

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Question 30 Unsaved
What is the net force acting on a golf car traveling at a constant speed of 5 mph?

0 N

10 N

5 N

15 N

Answers

If the speed is constant, there is no acceleration. No acceleration, no force.

A net force is defined as the sum of all the forces acting on an object. The equation below is the sum of N forces acting on an object. There may be several forces acting on an object, and when you add up all of those forces, the result is what we call the net force acting on the object.

So likely your answer going to be c.

Please make me brainliest.

Is this triangle a right triangle?

Answers

no it is not

2^2 = 4
3^2 = 9
4^2 = 16

9+4 = 13
13 does not = 16

you can get help from Pythagoras theorem :
[tex] {x}^{2} = {2}^{2} + {3}^{2} \\ {x}^{2} = 4 + 9 = 13 \\ x = \sqrt{13} [/tex]
it's not a right triangle

PLEASE HELP WILL GIVE BRAINLIEST!!!******** William invested $7000 in an account that earns 4.5% interest, compounded annually.

Answers

This is a matter of plugging in numbers.
P = 7000 (starting value)
l = 0.045 (rate)
t = 3 (number of years)

A(t) = 7000(1 + 0.045)^3
A(t) = 7000(1.045)^3
After three years, William will have 7988.16

Marco drew 24 pictures he drew 1/6 of them in art class how many pictures did marco draw in art class

Answers

There are 24 pictures
If he drew 1/6 of them ⇒ he drew 1/6 of the 24

1/6 of 24 =1/6 x 24 = 4

So he drew 4 of them.

To find the answer, we need to multiply 24 by 1/6.

24 × 1/6 = 24/6 = 4

Marco drew 4 pictures in art class.

Hope this helps!

A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower. The wire makes an angle of 65° with the ground. Draw a diagram and find the length of the guy wire. 4.2 yd. 11.0 yd. 23.7 yd.

Answers

The wire, the tower and the ground will make a right triangle with hypotenuse that is equal to the length of the wire, the height that is equal to the height of the tower and the base that measures from the base of the building to point the wire has touched the ground.
The length of the wire will be given by:
cos θ = (adjacent)/(hypotenuse)
thus
cos 65=10/h
h=10/cos 65
h=23.66 yds~23.7 yds
the answer is 23.7 yd

Answer:

23.7 yards

Step-by-step explanation:

Given :A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower. The wire makes an angle of 65° with the ground

To Find: Draw a diagram and find the length of the guy wire

Solution :

Refer the attached figure

We are given that A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower i.e. AC = 10 yards

We are also given that wire makes an angle of 65° with the ground i.e. ∠BAC = 65°

Now to find the length of the guy wire i.e. AB

We will use trigonometric ratio.

[tex]cos\theta = \frac{Base}{Hypotenuse}[/tex]

[tex]cos 65 ^{\circ} = \frac{AC}{AB}[/tex]

[tex]0.4226= \frac{10}{AB}[/tex]

[tex]AB= \frac{10}{0.4226}[/tex]

[tex]AB= 23.66[/tex]

Thus AB = 23.66 yards ≈ 23.7 yards

Hence the length of the guy wire is 23.7 yards

simplify -1/2x+3-4x+5+3/2x

Answers

To simplify need to first solve the like terms which are the ones with the variable of X. Which gets you -3x. Then add your final terms which equals 8. And your simplifyed expression would be -3x + 8

Jack is learning to play piano. He knows that a piano has 88 keys and that there are 12 unique keys in each group called octave. How many complete octaves are on a piano?

Answers

There are seven full Octaves on a piano with 88 keys

Answer:

7 octaves

Step-by-step explanation:

Total number of keys in piano = 88 keys

Numbers of keys in each group called octave= 12 unique keys

We have to find the number of complete octaves on piano

Number of octaves consists of 12 keys= [tex]\frac{Total number of keys}{12}[/tex]

Number of octaves consists of 12 keys= [tex]\frac{88}{12}[/tex]

Number of octaves consists of 12 keys= 7 octaves

Hence, the correct answer is 7 octaves

Chris bought n packs of pencils. Each pack has 10 pencils. Write an equation to represent the total number of pencils p that Chris bought.

Answers

n = packs
p = number of pencils

equation: p = 10n

x= number of packs
P= total packs

Total packs equals pencils per pack times number of packs.

EQUATION:
P= 10x

Hope this helps! :)

CAN SOMEONE HELP (AND HELP ME UNDERSTAND)

Answers

Consider angle XZY in the attached figure. It is always 1/2 the measure of arc XY, no matter where Z may be located on the major arc XZY. This is true even when ZY is very short.

Now, consider what happens when Z falls on top of tangent point Y. The angle is still half the measure of arc XY, still 62°.

Selection C is appropriate.

_____
I apologize for any confusion caused by my choice of Z as the name of the point I added. Nothing in my explanation is intended to refer to the Z already shown in the unmodified figure.

Is 2 , -5 a solution to this system equation 2x + 5y = -19, 6y - 8x = -54 .? Justify your answer

Answers

The easiest way to solve this problem is to put (2, -5) into both equations and see if it satisfies/works for both of them. 2 = x and -5 = y.

So for 2x + 5y = -19,
2(2) + 5(-5) = -19
4 - 25 = -19
-21 ≠ -19.

You can continue and try it out for 6y - 8x = -54
6(-5) - 8(2) = -54
-30 - 16 = -54
-46 ≠ -54

But since (2, -5) already doesn't work for one equation, it cannot be a solution to the system of equations.

The annual interest rate on a loan is 10% which can be represented using the expression 1.10t. Write an expression that represents the quarterly interest rate.

Answers

Given that the interest rate is 10% which can be represented by 1.10t, the quarterly interested rate will be represented as follows:
annual rate=10%
quarterly rate=10/4=2.5%=0.025
given time t, this will be represented as :
(1+0.025)t
=1.025t

Consider the quadratic equation y^2-y=6. What is the error with the solution below?

Answers

I can not see any "solution below", I can offer you the solutions of the equation you gave

y^2-y-6=0 => y^2-3y+2y-6=0 => y(y-3)+ 2(y-3)=0 => (y-3) (y+2)=0

y-3=0 or y+2=0 => y=3 or y= -2

Check 1: 3^2 - 3 = 6 => 9-3=6 => 6=6 Identity prove solution
Check 2: (-2)^2 - (-2) =6 => 4+2=6 => 6=6 Identity prove solution

Good luck!!!!

The error in the given solution to the quadratic equation y²-y=6 is identified and corrected step by step.

In the given quadratic equation y²-y=6, the mistake in the solution provided is the incorrect manipulation of the equation. To find the correct solution, follow these steps:

Re-write the equation as y² - y - 6 = 0.

Factor the quadratic equation as (y - 3)(y + 2) = 0.

Solve for y by setting each factor to zero: y = 3 or y = -2.

The rectangular poster shown measures 2w-30 by w. The poster has an area of 5400 cm2. What is the value of w?

Answers

1. To solve this problem, you must use the formula of the area of a rectangle, which is shown below:

A=lxw

"A" is the area of the rectangle (A=5400 cm²).
"l" is the lenght of the rectangle (l=2w-30).
"w" is the width of the rectangle.

2. When you substitute l=2w-30 into the formula A=lxw, you have:

A=lxw
5400=(2w-30)(w)
5400=2w²-30w
2w²-30w-5400=0

3. Now you have a quadratic equation. When you solve it, you obtain the value of "w". Then:

w=60 cm

Convert the following decimal to a common fraction. Reduce to lowest terms 0.2 =

Answers

The answer is 1/5 hope this helps

The decimal conversion of 0.2 would be 2/10 since the decimal is rounded to the tenths place.

When finding the lowest terms of a fraction, you want to find the highest number that can go into both numbers, or greatest common factor (GCF), of both the numerator and the denominator. In this case, the greatest common factor would be 2, since it can go into both 2 and 10 without any remainders.

2 can go into 2 once, and into 10 five times, making the reduced term 1/5.

I hope I could help! Feel free to reach out if you need any more help with conversions and reductions.

Help with this math question please

Answers

Principal Amount = P = $ 4100
Interest rate = r = 7.25% = 0.0725
Time in years = t = 8 years
Amount accumulated = A

Formula for compound interest is:

[tex]A=P e^{rt} [/tex]

Using the given values, we get:

[tex]A=4100 e^{0.0725*8}=7322.76 [/tex]

Rounding of to nearest hundredth, the balance in the account after 8 years will be $7322.76

what is the solution of the equation sqrt 5x-7 = sqrt 3x+5 ?

Answers

[tex]\bf \sqrt{5x-7}=\sqrt{3x+5}\impliedby \textit{squaring both sides} \\\\\\ (\sqrt{5x-7})^2=(\sqrt{3x+5})^2\implies 5x-7=3x+5\implies 2x=12 \\\\\\ x=\cfrac{12}{2}\implies x=6[/tex]

x=6 loves because it just does

What will it cost to carpet a rectangular floor measuring 21 feet by 24 feet if the carpet costs $ 31.96 per square yard?

Answers

Area of a rectangle is equal to the base multiplied by the height. However, you are given the measurements in feet, and these must be divided by 3 to get yards.

21 becomes 7, and 24 becomes 8. 7/8 = 56 yards squared.

Multiplied by $31.96, the total comes out to $1789.76.

A farmer has harvested 60% of his crops. If he has harvested 72 acres, how many acres does the farmer have in all?

Answers

Answer:

120 Acres

Step-by-step explanation:

We want to find the total amount of acres that a farmer has given that we know how many acres are in a percentage of his farm.

The farmer has 120 acres in total.

We know that the 60% of the farmer crops is equivalent to 72 acres.

Now we want to find the 100%.

Then we write two equations:

100% = X

60% = 72 acres

Now we want to solve this for X.

To do it, we first take the quotient between the two equations:

100%/60% = X/(72 acres)

Now we solve this for X:

(100%/60%)*(72 acres) = X = 120 acres.

The farmer has 120 acres in total.

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Which is a counterexample to this conjecture? The sum of any two consecutive integers is a composite number. A. 16 + 17 = 33 B. 10 + 11 = 21 C. 6 + 7 = 13 D. 7 + 8 = 15

Answers

C. 6 + 7 = 13

This is because 33, 21, and 15 are composite numbers, and 13 is not.

Final answer:

The sum of two consecutive integers being composite is disproved by the example 7 + 8 = 15, which is prime.

Explanation:

Counterexample: The sum of any two consecutive integers being a composite number is disproved by the example: 7 + 8 = 15, which is a prime number and not composite.

Explanation: A composite number is a positive integer that has more than two distinct positive divisors. In the case of 7 + 8 = 15, 15 only has divisors 1 and 15, making it a prime number, not composite.

Understanding Conjectures: Counterexamples are essential in mathematics to disprove conjectures by showing cases where the given rule or statement does not hold true.

each side of a square shaped room is 7 ft long what is the rooms area

Answers

think of it this way 7x4=28 cause u have 7and ur basically adding 7 four times

Hello!

A square has four sides, and they have the same length. We must use a formula to calculate the area of a square. The formula is:

A = s^2

It's just the sides squared.

Each side is 7 feet long.

Substitute:

A = 7^2

A = 49

ANSWER:

The area of the room is 49 ft squared.

*Put a small 2 at the end of "ft" to indicate that it is squared!

Two jets leave an airport at the same time, flying in opposite directions. The first jet is traveling at three hundred seventy-seven mph and the other at two hundred seventy-five mph. How long will it take for the jets to be 9128 miles apart?

Answers

Remember that distance equals speed times time: [tex]d=st[/tex]. We know for our problem that the speed of our first jet is 377 mph, so [tex]s_{1}=377[/tex]. We also know the speed of our second one is 275 mph, so [tex]s_{2}=275[/tex]. Since the the time that will it take for the jets to be 9128 miles apart is the same, [tex]t[/tex] is going to be equal for both jets. Now we can setup our distance equations for both jets.
For our first jet:
[tex]d_{1}=377t[/tex]
For our second jet:
[tex]d_{2}=275t[/tex]

We know for our problem that after [tex]t[/tex] the jets will be 9128 miles apart, so the total distance will be 9128: [tex]d_{t}=9128[/tex]. Since our jets are traveling in opposite directions, the distance between them will increase over time, so we are going to add [tex]d_{1}[/tex] and [tex]d_{2}[/tex], and set them equal to [tex]d_{t}[/tex] to find our time:
[tex]d_{t}=d_{1}+d_{2}[/tex]
[tex]9128=377t+275t[/tex]
[tex]9128=652t[/tex]
[tex]t= \frac{9128}{652} [/tex]
[tex]t=14[/tex]

We can conclude that our jets will be 9128 miles apart after 14 hours.

Final answer:

To find the time it takes for two jets to be 9128 miles apart, calculate their combined speed and divide the total distance by this speed, resulting in approximately 14 hours.

Explanation:

To find the time taken for the jets to be 9128 miles apart:

Calculate the combined speed of the two jets by adding their speeds together: 377 mph + 275 mph = 652 mph.

Divide the total distance of 9128 miles by the combined speed of the jets to get the time taken: 9128 miles ÷ 652 mph ≈ 14 hours.

Other Questions

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