Question

While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is After you drive 17 miles closer to the mountain, the angle of elevation is Approximate the height of the mountain.

Answer 1

The mountain height is 1.025 miles.

Explanation:

Due to the movement of the observer, there are two different positions, x and 17+x.

For the first triangle, the first angle 2.5° is directly opposite the mountain height and it has a base of 17+x.

Similarly, for the second triangle, the second angle 9° is also directly opposite the mountain height and it has a base of x.

Thus:

Tan 2.5° = h/(17+x) and h = Tan 2.5°(17+x)

Tan 9° = h/x and h = Tan 9°(x)

Therefore, Tan 2.5°(17+x)=Tan 9°(x)

0.0437(17+x) = 0.1584x

0.1584x-0.0437x = 0.7429

x = 6.48 miles

h = Tan 9°(x) = Tan 9°(6.48) = 1.03 miles

Thus the mountain height is 1.03 miles.