Question

At a certain point on a cliff-face, a rock-climber, Rob, observes the base of the cliff opposite to have an angle of depression of 60'. He also observes the top of the same cliff to have an angle of elevation of 40°. He knows that the distance from the base of the cliff he is climbing to the base of the opposite cliff is 110m. If the cliff that Rob is climbing is 30 m taller than other, find the height of the smaller cliff.​

Answer 1

283 m

Explanation:

The tangent relation is useful for this.

Tan = Opposite/Adjacent

This tells us the distance from Rob's height to the ground on the other cliff is ...

tan(60°) = CB/CA

CB = CA·tan(60°) = 110·tan(60°)

Similarly, ...

tan(40°) = CD/CA

CD = CA·tan(40°) = 110·tan(40°)

Then the height of the smaller cliff is ...

BD = CB +CD = 110·(tan(60°) +tan(40°)) ≈ 282.8 m

The height of the smaller cliff is about 283 m.