From the top of the control tower 250 m tall, an airplane is sighted on the ground below. If the airplane is 170 m from the base of the tower, find the angle of depression of the airplane from the top of the control tower.

Tan= Opposite/Adjacent

Tan ß = 250m/170m

Tan ß = 1.470588235

Since we are looking for angle theta's value, we need to press:

Shift+Tan+1.470588235 = 55.78429786 m is the angle of depression of the airplane from the top of the control tower.

(Sorry, I can't show you how the right triangle or the figure will look like. But we should always answer in a complete sentence of atleast label you answer. Peace.)

YEs

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base ———————— boat
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airplane

Tan= Opposite/Adjacent
Tan ß = 250m/170m
Tan ß = 1.470588235

Since we are looking for angle theta's value, we need to press:
Shift+Tan+1.470588235 = 55.78429786 m is the angle of depression of the airplane from the top of the control tower.

(We should always answer in a complete sentence of atleast label you answer. Peace.)

To find the angle of depression, we need to use trigonometry. The angle of depression is the angle between the horizontal line and the line of sight from the top of the control tower to the airplane on the ground.

Let's label the right triangle formed by the control tower, the airplane, and the ground. The height of the control tower is the opposite side of the triangle, and the horizontal distance from the base of the tower to the airplane is the adjacent side. We want to find the angle, which is the angle of depression.

We can use the tangent function to find the angle of depression. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the tangent of the angle of depression is equal to the height of the control tower divided by the horizontal distance to the airplane.

So, we have:

tan(θ) = height of the control tower / horizontal distance

Plugging in the values:

tan(θ) = 250 m / 170 m

Now, we can use a scientific calculator or trigonometric table to find the value of θ. To do this, we need to find the inverse tangent (or arctan) of the ratio:

θ = arctan(250/170)

Using a calculator, we find that θ is approximately 53.13 degrees.

Therefore, the angle of depression of the airplane from the top of the control tower is approximately 53.13 degrees.

10.0

From the top of the control tower 250 m tall, an airplane is sighted on the ground below. If the airplane is 170 m from the base of the tower, find the angle of depression of the airplane from the top of the control tower

tan(Θ) = 250/170