an observer on a cliff 1200 feet above sea level sights two ships due East. The angle of depression to the shops are 48° and 33°. What is the distance between the ships?

Answers

Answer 1

Final answer:

The problem involves using trigonometry, specifically the tangent function, to determine the distance between the two ships. By calculating the distance from the observer to each ship separately and finding the difference, we find the distance between the two ships to be approximately 814.61 feet.

Explanation:

The problem at hand involves the use of trigonometry, specifically tangent of an angle in a right triangle. Since we are dealing with angles of depression, we must understand that these angles are taken from a horizontal line - in this case, the line of sight from the cliff's edge.

First, let's consider the observer and the further away ship using tangent as follows:

tangent of 33° = height/distance, thus distance to the further ship = height / tangent of 33° = 1200 / tan(33) approximately equals to 1809.54 feet.

Similar steps for nearer ship with angle of 48 degrees:

tangent of 48° = height/distance, hence distance to the closer ship = height / tangent of 48° = 1200 / tan(48) approximately equals to 994.93 feet.

Therefore, the distance between the ships is the difference between the two distances calculated above, which will be 1809.54 - 994.93 = 814.61 feet.

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Answer 2

Final answer:

To determine the distance between the two ships, use the angles of depression and the observer's height above sea level to find the horizontal distances to each ship with trigonometry and subtract the smaller from the larger.

Explanation:

To calculate the distance between two ships using their angles of depression from an observer's viewpoint atop a cliff, we can employ trigonometry. Let us denote the observer's vertical distance above sea level as height (h), which is 1200 feet in this case. The angles of depression to the first and second ship are 48° and 33° respectively.

We will use the tangent of these angles to find the horizontal distances (d1 and d2) from the base of the cliff to each ship:

Using the tangent of the angle of depression 48° to find distance to first ship (d1):
tangent(48°) = opposite/adjacent or, h/d1
Thus, d1 = h / tangent(48°)Using the tangent of the angle of depression 33° to find distance to second ship (d2):
tangent(33°) = opposite/adjacent or, h/d2
Thus, d2 = h / tangent(33°)

After finding d1 and d2, we subtract the smaller distance from the larger to get the distance between the two ships:

Distance between ships = d2 - d1

Finally, we convert the answer from feet to the desired unit if necessary.

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Related Questions

Hello! I need a bit of help with this one! Thanks

of the calculators sold this week, 3/8 of them were blue and of those, 2/9 were broken. What fraction of the calculators were blue and broken?

Answers

so 2/9 of the 3/8 calculators were broken.

2/9 x 3/8 = 1/12 of the calculators were broken.

Sarah build a dollhouse the floor the dollhouses Square Sara covers the floor with 144 square inches of tile how long in inches is one side of the dollhouse floor?
A. 12
B. 38
C. 72
D. 144

Answers

All you have to do is find the square root of the area because the area is the side length squared.

square root of 144 = 12

So a side length is 12

A. 12x12 is 144 and the tile has to be a 12 by 12 to have 144 tiles.

40% of college students scored more than 70% on a math test 120 students scored below that how many total students took the math test

Answers

there were 200 students in total

1/4-(2006 + .20)+2x2-4

Answers

-2005.95. I googled it. May want to double-check though, and if you get something differentx let me know.

what is the answer to 50% of 4=

Answers

50% of 4 = 2 . . . . . .

!! 30 PTS !!
Hello, I need some help on this Geometry Area question:

Answers

You have to multiply 54 times 1.2 and you will get 64.8. So, 64.8 is your area.

Kenji's dog ate 3/12 of e treats in a box of dog treats on Monday. His dog ate 2/12 of the treats on Tuesday. What fraction more of the box of the treats did his dog eat on Monday than on Tuesday?

Answers

1/12 of the box of dog treats

3/12-2/12= 1/12

Larry has a cylinder shaped pitcher that is 13 inches long and a radius of 4 inches. Sandra has a cylinder shaped pitcher that is 8 inches long and a radius of 6 inches

Answers

The approximate volume of Sandra's pitcher is 904.78 cubic inches.

What is the volume of a right circular cylinder?

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

We are given that;

For Larry's picture, we have r = 4 inches and h = 13 inches. Substituting these values into the formula, we get:

V = π(4^2)(13)

V ≈ 804.25 cubic inches

Therefore, the approximate volume of Larry's picture is 804.25 cubic inches.

For Sandra's pitcher, we have r = 6 inches and h = 8 inches. Substituting these values into the formula, we get:

V = π(6^2)(8)

V ≈ 904.78 cubic inches

Therefore, the volume of cylinder will be 904.78 cubic inches.

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The complete question is;

Larry has a cylinder shaped pictures that is 13 inches long and radius of 4 inches. Sandra has a cylinder shaped pitcher that is 8 inches long and radius of 6 inches. The volume of Larry’s picture is approximately __. The volume of Sandra’s pitcher is approximately __?

Guys help me please:(

Answers

x = -2
y = -5
For this case, you must realize that the solution to the system of equations is the ordered pair:
(x, y) = (- 2, -5)
Graphically, they are two lines that intersect in the third quadrant.
Answer:
See attached image.

Need help! Stuck in this question.

Answers

this is the answer i got on this calculator

In the past you paid $800
per month to rent your apartment. You now pay $900
per month for your rent. What is the percent increase in your rent?

Answers

Hello! $800 was the past amount for rent and now it's $900. 900 - 800 is 100. that's a $100 difference. In order to find the percent increase in the rent, we can write and sovle a proportion. It would be set up as change/original = x/100, where change is difference between two numbers and original is the previous price. It would be set up like this:

100/800 = x/100

Let's crossmultiply the values. 100 * 100 is 10,000. 800 * x is 800x. That makes 10,000 = 800x. Now, divide each side by 800 to isolate the x. 800x/800 cancels out. 10,000/800 is 12.5 or 12.5%. Let's check this by multiplying by 112.5%. 800 * 112.5% (1.125) is 900. That's what we're looking for! There. x = 12.5%. The percent increase is 12.5%.

900-800=100.. 100/800=.125 . 125x100=12.5%

Simplify the expression so there is only one positive power for each base
(3^-2•7^-5)^-4

Answers

= 3^(-2*-4)*7*(-5*-4)= 3^8*7^20

D is the answer

Answer:The and is D

Step-by-step explanation:

A line containing the points (2, 16) and (-8, -4) intersects the y-axis at what point?

Answers

We first need to find the slope of this line: (-4-16)/(-8-2) = -20/-10 = 2.
We write this as slope-intercept: y = 2x + b(b is the y-intercept). Now we plug in on of the above points: 16 = 2(2) + b, and b is equal to 12.
---
Hope this helps!

Final answer:

To find the y-intercept of a line, we can use the equation y = mx + b. By substituting the coordinates of one of the given points into the equation, we can solve for b and find the y-intercept. The y-intercept is the point where the line intersects the y-axis.

Explanation:

The line containing the points (2, 16) and (-8, -4) can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we need to substitute the values of one of the given points into the equation and solve for b.

Using the point (2, 16), we have 16 = m(2) + b. Substituting the values of the other point gives us -4 = m(-8) + b. We can solve this system of equations to find the values of m and b.

16 = 2m + b-4 = -8m + b

By subtracting equation 2 from equation 1, we can eliminate b and solve for m. After finding the value of m, we can substitute it back into either equation to find the value of b. This will give us the y-intercept.

Once we have the values of m and b, we can write the equation of the line in the form y = mx + b. The y-intercept will be the point at which the line intersects the y-axis.

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Which equation best describes the line of best fit?

A) y=6x +10

B) y=x−10

C) y=10x +70

D) y=2/3x

Answers

The y-value changes from 10 to 70 as the x-value changes from 0 to 10. That makes the slope (70 -10)/(10 -0) = 6, and the y-intercept = 10.

Selection A is the appropriate equation.

what quadrilateral has exactly one pair of parallel sides

Answers

Trapezoid because it has 4 sides and one pair of parallel sides and one pair of non parallel sides

The answer is a trapezoid

How does the height of the triangle compare to the height of the rectangle

Answers

The triangle's height must be 3 times that of the rectangle for the areas to be the same.

For a triangle, A = (1/3)bh
For a rectangle, A = bh

If we let h represent the height of the rectangle and H represent the height of the triangle, we have
.. (1/3)bH = A = bh
.. H = 3h . . . . . . multiply the above equation by 3/b

What are the operations used to
solve this equation5/6x-2=-2/3x+1

Answers

addition
multiplication

Which shows a correct order to solve this story problem?

Simone was arranging a party for some friends. She needed 25 balloons and 12 packs of napkins. Napkins cost $4.50 per pack and balloons cost $0.75 each.

How much money did Simone spend?

A.

Step 1: Multiply $0.75 by 12.

Step 2: Multiply $4.50 by 25.

Step 3: Add the two products.

B.

Step 1: Add $0.75 and 12.

Step 2: Add $4.50 and 25.

Step 3: Multiply the two sums.

C.

Step 1: Multiply $0.75 by 25.

Step 2: Multiply $4.50 by 12.

Step 3: Add the two products.

D.

Step 1: Calculate the cost of 1 napkin.

Step 2: Multiply $0.75 by 25.

Step 3: Add the two numbers together.

Answers

Selection C represents the way the costs would be added at the store.

How do u solve this system with substitution?

Answers

4x - (2x - 5) = 7

4x - 2x + 5 = 7

2x + 5 = 7

2x = 2

x = 1

y = 2(1) - 5

y = 2 - 5 = -3

Evaluate sin[2 arccos( -8/17 )].

Answers

Recall that [tex]\sin2x=2\sin x\cos x[/tex], so that

[tex]\sin\left(2\arccos\left(-\dfrac8{17}\right)\right)=2\sin\left(\arccos\left(-\dfrac8{17}\right)\right)\cos\left(\arccos\left(-\dfrac8{17}\right)\right)[/tex]

Dealing with the cosine terms is simple, since [tex]\cos(\arccos x)=x[/tex] (so long as [tex]0\le \arccos x\le\pi[/tex], which is true here). So

[tex]\cos\left(\arccos\left(-\dfrac8{17}\right)\right)=-\dfrac8{17}[/tex]

To find the sine, we can make a substitution of [tex]\theta=\arccos\left(-\dfrac8{17}\right)[/tex]. In other words, we suppose that [tex]\theta[/tex] is some angle that satisfies [tex]\cos\theta=-\dfrac8{17}[/tex].

If this is the case, then we have

[tex]\sin^2\theta=1-\cos^2\theta=\dfrac{225}{289}\implies\sin\theta=\pm\sqrt{\dfrac{225}{289}}=\pm\dfrac{15}{17}[/tex]

But which value do we choose? We know that [tex]\cos\theta[/tex] is negative, which means [tex]\theta[/tex] must be between [tex]\dfrac\pi2[/tex] and [tex]\pi[/tex]. The sine of any angle [tex]\theta[/tex] in this interval will always be positive, so in fact

[tex]\sin\theta=\sin\left(\arccos\left(-\dfrac8{17}\right)\right)=\dfrac{15}{17}[/tex]

Putting everything together, we get

[tex]\sin\left(2\arccos\left(-\dfrac8{17}\right)\right)=2\left(\dfrac{15}{17}\right)\left(-\dfrac8{17}\right)=-\dfrac{240}{289}[/tex]

EXPLAIN HOW A NUMBER LINE CAN BE USED TO FIND THE DIFFERENCE
FOR 34-28

Answers

You can count the marks on the line + the lower number to have the answer of 14

A number line can help you solve this equation because it can specifically tell the exact spots between the numbers and you can easily get the answer without checking your answer!

please help im confused

Answers

25) It is a right triangle

3²+4²=5²
9+16=25
25=25

26) It is a right triangle

6²+8²=10²
36+64=100
100=100

27) Not a right triangle

5²+5²=10²
25+25=100
50=100

28) It is a right triangle

5²+12²=13²
25+144=169
169=169

Hope this helps :)

Emma buys a game for $26.84. She pays for the game with a $20 bill and two $5 bills.
How much change should she receive? - $3.16
List the change in coins and bills. - ??

Answers

3 one dollar bills
One dime
6 pennies

if the length of FH is 18 units, what is the value if x

Answers

Answer:

The value of x is 3

Step-by-step explanation:

Given that the length of FH is 18 units

we have to find the value of x.

Point G lies between F and H in which measurements are

[tex]\text{FG=4x and GH=2x}[/tex]

[tex]FH=4x+2x=6x\thinspace units[/tex]

[tex]6x=18[/tex]

Divide by 6 throughout the equation.

[tex]x=\frac{18}{6}=3[/tex]

The value of x is 3 cm.

Option 1 is correct.

You are buying salsa at the grocery store. You have a manufacturer’s coupon for $0.50 off and the store is offering 50% off if you buy 2 containers. One container of salsa costs $3.25. What is your final cost?

Answers

3.25*2 = 6.5*0.5 = 3.25-0.50 = $2.75

Answer: Final cost will be $2.75.

Step-by-step explanation:

Since we have given that

Cost of salsa container = $3.25

Off on coupon = $0.50

Final cost of one salsa container is given by

[tex]3.25-0.50\\\\=\$2.75[/tex]

Hence, the final cost will be $2.75.

if he bought two containers

Cost of two containers is given by

[tex]3.25\times 2\\\\=\$6.50[/tex]

Coupon 50% off is given by

[tex]6.50\times 0.5\\\\=3.25[/tex]

So, Final cost is given by

[tex]6.25-3.25-0.5\\\\=\$2.75[/tex]

Hence, Final cost will be $2.75.

Answer this correctly plz

Answers

The area of the triangle is
  A = (1/2)bh
  = (1/2)(3 ft)(6 ft)
  = 9 ft^2

That triangular area is not carpeted, so the carpet area is
  72 ft^2 -9 ft^2 = 63 ft^2.

Worth 25 POINTS HELP ASAP
(Picture is shown!)

Answers

Your answer is 1 and 2/5

3 - 1 3/5= 1 2/5 or 1.4

first u simplify 1 3/5 which is 8/5

the expression turns into 3 - 8/5

3 8 2
_ - _ = 1 _
1 5 5

to answer, u have to find a gcf to find the common denominators.

15/5 - 8/5 = 7/5
7/5 = 1 2/5

or

u can put them into decimal:

3 - 1.6 = 1.4
1.4 = 1 2/5
(4/10 simplified is 2/5)

so, the answer is 1 2/5 or 1.4

Find the value of X in the triangle.

Please explain. Thanks.

Answers

29°

triangles can only have 180°

This is a right triangle, so one angle is 90°, leaving us with 90° left

90°-61°= 29°

X=29
You have a right angle, they're always 90 degrees, plus 61 degrees = 151, next you subtract 151 from 180 = 29 degrees.

Which model is most appropriate for the data shown in the graph below

Answers

it's an exponential graph.

it is an Exponential graph

Leslie drank 4/5 pint of juice and Hank drank 7/10 pint of juice. Who drank more

Answers

Leslie did. If you multiply 4/5 by two, you get 8/10. 8/10 is greater than 7/10.

Leslie, since 4/5 is equal to 8/5 (multiply the top and bottom by two, to have the same denominator as 7/10) which is greater than, 7/10

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