Question

Matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on the lake is 42 degrees. How far is the boat from the base of a cliff?

Answer 1

1. Matt is standing on a cliff of height 305 feet

2. Depression angle is 42 degrees

3. So considering boat to be a vertex of triangle and cliff height as a side of triangle then joining the vertex to both the sides by using straight lines we get a triangle with upper angle value as 42 degrees

4. Using Tan(tita) with tita as angle of depression we get Tan(tita) = Distance of boat from cliff by height of cliff

5. Substituting the values we get Tan(42degrees) = 0.9

6. Multiplying 0.9 with 305 we get 274.62 feet

7. So boat is 274.62 feet far from the cliff