Question

In traveling across flat land, you see a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive 19 kilometers closer to the mountain, the angle of elevation is 9° (see the following figure).
Approximate the height of the mountain (in kilometers). (Round your answer to one decimal place.)

Answer 1

The height of the mountain is 0. 2 km

How to determine the height

First, let's find the hypotenuse of the second triangle

Using the tangent identity, we have;

tan θ = opposite/ adjacent

tan 3. 5 = x/ 19

cross multiply

x = tan 3 . 5 × 19

x = 0. 061 × 19

x = 1. 16 km

Now, we have the hypotenuse side of the second triangle and we need to find the opposite side which is the height of the mountain

Using the sine identity:

sin 9 = y/ 1.16

cross multiply

y = sin 9 × 1. 16

y = 0. 1564 × 1. 16

y = 0. 18 km

y = 0. 2 km in one decimal place

Thus, the height of the mountain is 0. 2 km

Learn more about angle of elevation here:

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