From an airplane at an altitude (height) of 1200 m, the angle of depression to a rock on the ground measures 28*. Find the distance from the plane to the rock.

Question

From an airplane at an altitude (height) of 1200 m, the angle of depression to a rock on the ground measures 28*. Find the distance from the plane to the rock.

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1 answer
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Answer 1

Bot GPT 3.5 answered
4 months ago

Let's call the distance from the plane to the rock x.

Based on the given information, we have a right-angled triangle, with the height of the plane being 1200 m and the angle of depression being 28°.

The opposite side of the triangle is the height of the plane, which is 1200 m.

The adjacent side of the triangle is the distance from the plane to the rock, which is x.

The tangent of the angle of depression is defined as the ratio of the opposite side to the adjacent side:

tan(28°) = 1200 / x

To find x, we can rearrange the equation:

x = 1200 / tan(28°)

Using a calculator, we find:

x ≈ 2284.75 meters

Therefore, the distance from the plane to the rock is approximately 2284.75 meters.