A plane is flying at an altitude of 12000 m. From the pilot the angle of depression to the airport tower is 32°. How far is the tower from the point directly beneath the plane? Round to the nearest thousandth.

Question

A plane is flying at an altitude of 12000 m. From the pilot the angle of depression to the airport tower is 32°. How far is the tower from the point directly beneath the plane? Round to the nearest thousandth.

Answer 1

The solving procedure is correct but:

tan 32 ° = 0.624869352

12000 / tan 32 ° = 12000 / 0.624869352 = 19204.0143457 m

19000 m
rounded to the nearest thousandth.

Answer 2

To find the distance from the tower to the point directly beneath the plane, we can use trigonometry.

Let's label the distance we are trying to find as "x".

We have an angle of depression of 32°, which means that the angle formed between the horizontal ground and the line connecting the tower to the point beneath the plane is also 32°.

Using the trigonometric function tangent (tan), we can set up the equation:

tan(32°) = x / 12000 m

To solve for x, we can rearrange the equation as follows:

x = tan(32°) * 12000 m

Now, let's calculate the distance x.

Using a calculator, calculate the tangent of 32°:

tan(32°) ≈ 0.62487

Then, multiply this value by 12000 m:

x ≈ 0.62487 * 12000 m

x ≈ 7498.44 m

Therefore, the tower is approximately 7498.44 meters away from the point directly beneath the plane, rounded to the nearest thousandth.

Answer 3

To find the distance from the tower to the point directly beneath the plane, we can use trigonometry. Specifically, we can use the tangent function.

Let's call the distance we want to find "x".

First, let's draw a diagram to visualize the situation. we have a right triangle formed by the plane, the tower, and the point directly beneath the plane.

The angle of depression is the angle formed between the line of sight from the pilot to the tower and a horizontal line at the level of the plane. In this case, the angle of depression is 32°.

Now, we can use the trigonometric identity:

tan(angle) = opposite/adjacent

In this case, opposite is the height of the plane (12000m), and adjacent is the distance we want to find (x).

So, we can write:

tan(32°) = 12000 / x

To find x, we can rearrange the equation:
x = 12000 / tan(32°)

Using a calculator, we can find:

x ≈ 20680.670

Therefore, the tower is approximately 20,680.670 meters from the point directly beneath the plane.

Answer 4

tan^=p/b

tan32°=12000/b
0.62=12000/b
(0.62×b)=12000
b=12000/0.62
b=19354.83871m