A pilot approaching a 3000-meter runway finds that the angles of depression of the ends of the runway are 14° and 20°. How far is the plane from the closer end of the runway? Round to the nearest tenth place.

Answers

Answer 1

Final answer:

To find out how far the plane is from the closer end of the runway, we use the angles of depression and runway length to calculate the distance using trigonometric ratios. The distance is found to be approximately 26153 meters.

Explanation:

To determine the distance from the plane to the closer end of the runway, we use trigonometric ratios based on the angles of depression given. The angles of depression to the ends of the runway are 14° and 20°. Since the problem involves a horizontal surface (runway) and vertical angles (angles of depression), we can create two right triangles. One triangle has an angle of 14° between the plane's line of sight and the horizontal surface, and the other one has a 20° angle.

Let x be the distance from the plane to the point directly above the closer end of the runway and y be the distance from the plane to the point directly above the far end of the runway. We are looking for x, which can be found using the tangent of the 14° angle.

x = runway length / (tan(20°) - tan(14°))

Given the runway length as 3000 meters, we can calculate:

x = 3000 / (tan(20°) - tan(14°))

Crunching the numbers:

x ≈ 3000 / (0.3640 - 0.2493)

x ≈ 3000 / 0.1147

x ≈ 26153 meters (rounded to the nearest tenth)

Therefore, the distance from the plane to the closer end of the runway is approximately 26153 meters.

Related Questions

Find the sum of the measures of the interior angles of a convex 14-gon.

Answers

sum of all interior angles = (n-2)x180, n being the number of sides.

sum of all interior angles = (n-2)x180
sum of all interior angles = (14-2)x180
sum of all interior angles = 12 x180
sum of all interior angles = 2160°

Final answer:

The sum of the interior angles of a convex 14-gon is calculated using the formula (n - 2) × 180°, which equals 2160°.

Explanation:

The sum of the interior angles of any polygon can be found using the formula (n - 2) × 180°, where n is the number of sides. For a convex 14-gon, we plug in 14 for n in the formula to find the sum:

sum of all interior angles = (n-2)x180, n being the number of sides.

Sum = (14 - 2) × 180°

Sum = 12 × 180°

Sum = 2160°

This calculation shows that the sum of the interior angles of a convex 14-gon is 2160 degrees.

Which parent function has a constant slope?

A. linear
B. square root
C. quadratic
D. exponential

Answers

The slope of a line is the tangent of the angle that forms the line with the positive direction of the abscissa axis.
We note that for linear functions, this value is always the same.
The standard equation of the line is:
y = mx + b
Where,
m = slope of the line.
This value is always the same regardless of the domain of the function.
Answer:
A parent function that has a constant slope is:
A. linear

Anna and Bill share some money in the ratio 2:5
Anna gets £A
Bill gets £B
Carl and Donna share twice as much money as Anna and Bill share.
They share the money in the ratio 3:1
Carl gets £C
Donna gets £D
Find A:B:C:D in its simplest form

Answers

let the total amount of money that Anna and Bill shared be £ x
amount of money Anna received will be £A=2/7x
amount of money Bill received will be £B=5/7x
let the total amount of money that Carl and Donna shared be £ 2x
amount of money received by Carl is £C=3/4(2x)=3/2x
amount of money received by Donna is £D=1/4(2x)=1/2x
the ratio of money received by them altogether will be:A:B:C:D
this is equal to:
2/7x:5/7x:3/2x:1/2x
this can be simplified to:
2/7:5/7:3/2:1/2
this can further be simplified to:
(2/7*14):(5/7*14):(3/2*14):(1/2*14)
hence we shall have:
4:10:21:7

The ratio A:B: C:D in its simplest form is 4:10:15:5.

Let's denote the total amount of money shared by Anna and Bill as M. Since Anna and Bill share this money in the ratio of 2:5, Anna gets 2/7 of M and Bill gets 5/7 of M.

So, we have:

Anna's share (A) = (2/7)M

Bill's share (B) = (5/7)M

Carl and Donna share twice as much money as Anna and Bill, which means the total amount of money shared by Carl and Donna is 2M. They share this money in a ratio of 3:1.

Therefore:

Carl's share (C) = (3/4)(2M) = (3/2)M

Donna's share (D) = (1/4)(2M) = (1/2)M

Now, we want to find the ratio A:B:C: D. To do this, we need to express all shares in terms of the same unit. Since Anna and Bill's total money is M, we will express Carl and Donna's shares in terms of M as well.

We have:

A = (2/7)M

B = (5/7)M

C = (3/2)M

D = (1/2)M

To find the ratio A:B: C:D, we can compare the coefficients of M:

A:B:C:D = (2/7)M : (5/7)M : (3/2)M : (1/2)M

To simplify this, we can multiply each term by the least common multiple (LCM) of the denominators, which is 14. This will give us the ratio in whole numbers without changing the proportions.

Multiplying each term by 14, we get:

A:B:C:D = (2/7)*14 : (5/7)*14 : (3/2)*14 : (1/2)*14

A:B: C:D = 4:10:15:5

Therefore, the simplest form of the ratio A:B: C:D is 4:10:15:5.

the sum of 4 times a number and -5 added to 9 times number

Answers

4 * (n*9) -5
Use PEMDAS

Which triangle is a regular polygon? A) All triangles B) An equiangular triangle C) 45°- 45° - 90° triangle D) 30°- 60° - 90° triangle

Answers

I need he picture of it to get know the angle

Answer:

its B

Step-by-step explanation:

The Pythagorean theorem describes the relationship between the lengths of legs a and b and the hypotenuse c of any right triangle.

a 2 + b 2 = c 2

Complete the equation below by writing an expression equivalent to the length of a, the leg of a right triangle.

Answers

Sorry. I should have known.
a = square root of (c^2 - b^2)
Does your marker let you omit the ^ meaning power of?
Be careful about how you enter that.
I don't think it would be correct to write square root of (c 2 - b 2) but maybe you can do that if you and your marker have agreed on it.

Answer: a = square root of (c^2 - b^2)

Step-by-step explanation:

Suppose the number of gallons of gasoline per day used by a car is normally distributed with a mean of 2.2 gallons and a standard deviation of 1.2 gallons.

What is the difference in gallons per day used by a car with a z-score of 3 and another car that has a z-score of 0?

A. 1.2

B. 2.6

C. 3.6

D. 4.6

Answers

The difference in gallons per day used is 3.6.

The formula to calculate a z-score is:
[tex]z=\frac{X-\mu}{\sigma}[/tex],

where X is the value used to calculate the score, μ is the mean and σ is the standard deviation. We have the z-scores so we must work backward:

[tex]3=\frac{X-2.2}{1.2}\text{ and }0=\frac{X-2.2}{1.2}[/tex]

For both equations, we will cancel the 1.2 by multiplying both sides:
[tex]3\times1.2=(\frac{X-2.2}{1.2})\times1.2\text{ and }0\times1.2=(\frac{X-2.2}{1.2})\times1.2 \\ \\3.6=X-2.2\text{ and }0=X-2.2[/tex]

Now we will cancel 2.2 from both equations by adding it to both sides:

3.6+2.2=X-2.2+2.2 and 0+2.2=X-2.2+2.2
5.8=X and 2.2=X

The difference in gas used per day would be given by
5.8-2.2 = 3.6.

From a barrel of colored marbles, you randomly select 4 blue, 5 yellow, 6 red, 2 green, and 5 purple marbles. Find the experimental probability of randomly selecting a marble that is not blue. A. The term shows 6 over 13. B. one-half C. start fraction 9 over 11 end fraction D. three-eighths

Answers

Hey,
It would be A
i just learned this 4 weeks ago in math class.

The required, experimental probability of randomly selecting a marble that is not blue is 9/11. Option C is correct.

What is probability?

Probability can be defined as the ratio of favorable outcomes to the total number of events.

The total number of marbles in the barrel is:

4 blue + 5 yellow + 6 red + 2 green + 5 purple = 22 marbles

The number of marbles that are not blue is:

5 yellow + 6 red + 2 green + 5 purple = 18 marbles

Therefore, the experimental probability of randomly selecting a marble that is not blue is:

18 marbles / 22 marbles = 9/11

Thus, the answer is option C: 9 / 11.

Learn more about probability here:

brainly.com/question/14290572

#SPJ3

A delivery person is scheduled to pick up 9 crates of patio pavers. Each crate weighs 14 ton. How much weight will the delivery person need to plan for?

Answers

9×14
which equals
126
Hope I helped :)

if a crate weights 14 tons, and we 9 crates
9*14=126 tons

Lexi bought 1 2/5 of green grapes and 2 3/10 of red grapes. Grapes are 2.99 a pound.Did lexi spend more or less then $12?

Answers

Less. If you multiple 1 2/5 by $2.99 you would get about $4.19. If you multiple 2 3/10 by $2.99 you would get about $6.88. If you add those together, you would get $11.07, which is less than $12.

A fire fighter has to get to a burning building as quickly as he can. there are three paths that he can take. he can take his fire engine over a large hill (5 miles) at 10 miles per hour. he can take his fire engine through a windy road (7 miles) at 9 miles per hour. or he can drive his fire engine along a dirt road which is 8 miles at 12 miles per hour.

Answers

Final answer:

The firefighter should take the path over the large hill as it will take the shortest amount of time to reach the burning building.

Explanation:

The firefighter has three paths to choose from in order to reach the burning building:

Path 1: The firefighter can take the fire engine over a large hill, which is 5 miles long, at a speed of 10 miles per hour.

Path 2: The firefighter can take the fire engine through a windy road, which is 7 miles long, at a speed of 9 miles per hour.

Path 3: The firefighter can drive the fire engine along a dirt road, which is 8 miles long, at a speed of 12 miles per hour.

The firefighter will need to calculate the time it takes to travel each path and choose the path that allows him to reach the burning building quickest.

Let's calculate the time for each path:

Path 1: Time = Distance / Speed = 5 miles / 10 miles per hour = 0.5 hours = 30 minutes

Path 2: Time = Distance / Speed = 7 miles / 9 miles per hour ≈ 0.78 hours ≈ 47 minutes

Path 3: Time = Distance / Speed = 8 miles / 12 miles per hour ≈ 0.67 hours ≈ 40 minutes

Based on the calculations, the firefighter should take Path 1 over the large hill, as it will take him the shortest amount of time to reach the burning building.

Select the situation in which one quantity is changing at a constant rate in relation to the other quantity.
Barry spends $9 on lunch daily.
The market value of a new computer decreases by 6% every year.
Nathan's investments increase in value by 13.5% each month.
The number of ants in a colony doubles every 8 weeks.

Answers

The number of ants in a colony doubles every 8 weeks.

Constant rate of change means that when the value of x increases, the y remains constant. So there is no change in the y value. In this case, the x value is the "week" and the y value is the "amount of ants".

Joe has some pocket money. He spends 90% of it. He has 50p left. How much pocket money did he have?

Answers

So he spent 90% of a number and had 50 left
£5. This is because 50p is 10%. To get 100% you therefore need to times 50p by 10, thus getting £5
Hope this helps!

Mae bought 15 football cards and 18 baseball cards. She seperated them into 3 equal groups.How many sports cards are in each group?

Answers

Total number of sports cards = 15 + 18 = 33

So if they are divided into 3 groups the number in each group = 33/3 = 11 cards Answer.

jenny said i'm thinking of fraction that is equivalent to 2/6 the numerator is 8 less than the denominator what fraction is jenney thinking of

Answers

The fraction 2/6 has a numerator that is 4 less than the denominator. If the numbers in the fraction are doubled, then their difference will be 8.

Jenny is apparently thinking of 4/12.

Each square on the grid represents 1 yd². What is the approximate area of this pond? A. about 10 yd² B. about 15 yd² C. about 20 yd² D. about 25 yd².

Answers

I think that C is the correct answer

What is the length of bc?

Answers

The length of BC is 15 units.

I used the Pythagorean theorem to find this. 8 is the length of the given leg, and 17 is the length of the hypotenuse:

8²+b²=17²
64+b²=289

Subtract 64 from both sides:
64+b²-64=289-64
b²=225

Take the square root of both sides:
√b²=√225
b=15

Solve by factoring. 5. X2 +11x + 10 = 0 6. X2 + 4x -32 = 0 7. 2x2 -21x -36 = 0 8. 3x2 + x -14 = 0 9. x2 – 4x =21 10. 2x2 -11x =-12

Answers

Hey there :)

5. x² + 11x + 10 = 0
Sum = 11
Product = 10
Factors = 1 and 10
( x + 1 )( x + 10 )
x = 1 , x = -10

6. x² + 4x - 32 = 0
Sum = 4
Product = -32
Factors = - 4 and 8
( x - 4 )( x + 8 )
x = 4 , x = -8

7. 2x² - 21x - 36 = 0
( 2x + 3 )( x - 12 )
x = [tex]- \frac{3}{2} [/tex] , x = 12

8. 3x² + x -14
( x - 2 )( 3x + 7 )
x = 2 , [tex]- \frac{7}{3} [/tex]

9. x² - 4x = 21
x² - 4x - 21 = 0
Sum = - 4
Product = - 21
Factors = - 7 and 3
( x + 3 )( x - 7 )
x = - 3 , x = 7

10. 2x² - 11x = -12
2x² - 11x + 12 = 0
( x - 4 )( 2x - 3)
x = 4 , x = [tex] \frac{3}{2} [/tex]

What is the area of the composite figure whose vertices have the following coordinates? (−2, −2) , (3, −2) , (5, −4) , (1, −8) , (−2, −4) Enter your answer in the box. units²

Answers

check the picture below.

notice the composite is just,

a 5x2 rectangle.

a triangle(yellow) with a base of 2 and a height of 2.

a triangle(red) with a base of 6 and a height of 4.

get the area of each, sum them up, and that's the area of the composite.

[tex]\bf \stackrel{rectangle}{(5\cdot 2)}~~~~+~~~~\stackrel{yellow~triangle}{\cfrac{1}{2}(2)(2)}~~~~+~~~~\stackrel{red~triangle}{\cfrac{1}{2}(6)(4)}[/tex]

While Joey was standing outside on a sunny day, his shadow was 5 feet long. The shadow of a nearby Oak tree was 12 feet long. If Joey is 6 feet tall, how tall is the Oak tree?

A. 15.6 feet

B. 14.4 feet

C. 10 feet

D. 13.4 feet

Answers

Shadow problems are usually solved with a proportion.
.. oak/(oak's shadow) = joey/(joey's shadow)
.. oak/(12 ft) = (6 ft)/(5 ft)
.. oak = (12 ft)*(6/5) = 14.4 ft . . . . . . . matches selection B

Describe the following sequence as arithmetic, geometric or neither.

2, 4, 6, 12, 14. . . .

I think it's arithmetic because it's +2, but then there's 6 to 12 and that's +6, but then it's back to +2 when it goes to 12 to 14.,

Answers

It can't be arithmetic. It can't be geometric, so it leads to it is neither.

In an isosceles triangle, the altitude and median are __________. I know they are the same but the same isn't one of the choices. These are the choices:
A. segments opposite one another
B. perpendicular segments
C. the same segment
D. the legs of the triangle,

Answers

C. The same segment. In an isosceles triangle, the altitude and the median are the same segments because they correspond to the base that is contained in the mediatrix of the base. This applies to equilateral and isosceles triangles and the demonstration is by the congruence of triangles.

1. Through music, literature, and painting, the romantic artists attempted to
(1 point)make people fall in love.

express their love for women.
stir the emotions.
get people to reject modern innovations.

2. What do the writers Walter Scott, Mary Shelley, Edgar Allen Poe, and William Wordsworth have in common?
(1 point)They were all men.
They were all French.

They were all English.

They were all romantic writers.

3. Romantic painters aimed to
(1 point)mirror the artist’s imagination.

re-create nature.
meet the highest standards of the École des Beaux-Arts.

f,

Answers

Romantic artists attempted to stir the emotions. The writers listed are all romantic writers. Romantic painters aimed to mirror the artist's imagination. In general, this was an artistic period driven by a focus on the feelings the artist and viewer experienced.

Trayvon sells candy bars at a price of $3 each. He purchases every order of 200 candy bars for $350. If the cost of shipping is $0.15 per bar, what is Trayvon’s profit function?

Answers

A profit function is the revenue function minus the cost function. Since the revenue will at R(x) = 3x and the cost will be at C(x) = -350 - 0.15x. The profit function will be equal to P(x) = 2.85x - 350 for the first 200 candy bars.

Which equation could have been used to create this graph?

A.
y = 5x

B.
y = x + 0

C.
y = x + 1

D.
y = x + 5

Answers

Im Pretty Sure its D!

Answer:

Its b :)

Step-by-step explanation:

Find the area of this trapezoid. All length measures are in centimeters.

Answers

we know that
The area of a trapezoid is given by the formula
Area=h*(b1+b2)/2
where
b1, b2 are the lengths of each base
h is the altitude (height)
Remember that the bases are the two parallel sides of the trapezoid. The altitude (or height) of a trapezoid is the perpendicular distance between the two bases

therefore
[area of trapezoid]=(11+5)*4/2--------> 64/2------> 32 cm²

the answer is 32 cm²

Help me please y’all

Answers

To solve for the inverse of a function, you have to interchange the variables x and y and solve for the value of y in terms of x:

F(x) = 5x/3 + 5

y = 5x/3 + 5

Interchange x and y:

x = 5y/3 + 5

Solve for the value of y in terms of x:

x – 5 = 5y/3

5y = 3 (x – 5)

y = 3 (x -5) / 5

f^-1 (x) = 3 (x -5) / 5

simplify the square root of 27x^12/300x^8

Answers

The first thing we are going to do is rewrite the expression correctly.
We have:
root (27x ^ 12 / 300x ^ 8)
Rewriting:
root ((27/300) * (x ^ 12 / x ^ 8))
root ((9/100) * (x ^ (12-8)))
root ((9/100) * (x ^ (4)))
root ((9/100) * (x ^ (4)))
3 * x ^ 2 * root ((1/100)
(3 * x ^ 2) / 10
(3/10) * (x ^ 2)
Answer:
(3/10) * (x ^ 2)

Answer:

3/10 x^2

Step-by-step explanation:

Side ab in triangle abd corresponds to which side of triangle abc? ab bc ac

Answers

Answer:

The correct answer to this question going by the reference photo is AC (answer) that corresponds to AB.

Step-by-step explanation:

Answer:

it is AC

Step-by-step explanation:

option c

Use the answer from the previous task to determine P(z < −2.1).
0.01790.58320.98211

Answers

Answer:

A on Edg :)

Step-by-step explanation:

Using the normal distribution, it is found that P(z < −2.1) = 0.0179.

Normal Probability Distribution

The z-score of a measure X in a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure X is from the mean, if it is positive above the mean, if it is negative below. After finding the z-score, the z-score table gives the p-value of this z-score, which is the percentile of the measure X.

From the z-table, we have that Z = -2.1 has a p-value of 0.0179, hence P(z < −2.1) = 0.0179.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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