Question

You are standing at the edge of a cliff. You look down with an angle of depression of 20 degrees and see a a dog at the bottom that is 130 feet away from where you're standing. What is the height of the cliff? Round your answer to the nearest tenth, and round only once.

Answer 1

Answer:

47.3feet

Step-by-step explanation:

The set up will give a right angled triangle.

The distance of the dog away from the cliff = 130 feet = adjacent side

Angle of depression = 20°

Height of the cliff = Opposite = x

Using the SOH, CAH, TOA trigonometry identity;

According to TOA;

tan theta = opposite/adjacent

tan 20 = x/130

Cross multiply;

x = 130tan20

x = 130(0.3639)

x = 47.3 feet

Hence the height of the cliff to the nearest tenth is 47.3feet