Question

A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 32 ∘ . From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 34 ∘ . How high (in feet) is the mountain?

Answer 1

To estimate the height of the mountain, we can use trigonometric ratios. By setting up and solving two equations involving the tangent of the angles of elevation, we can find the height of the mountain.

Step-by-step explanation:

To estimate the height of the mountain, we can use trigonometric ratios. Let's denote the height of the mountain as h. From the first point, we have an angle of elevation of 32°. This means that the tangent of 32° is equal to the height of the mountain divided by the distance from the observer to the mountain.

Using the trigonometric identity tangent θ = opposite/adjacent, we have:

tan(32°) = h/d

From the second point, we have an angle of elevation of 34° and a shorter distance from the observer to the mountain, which is 2000 feet closer. This gives us the equation:

tan(34°) = h/(d - 2000)

Now, we can solve these two equations simultaneously to find the value of h.