Imagine that you are standing at the top of a cliff that is 1,500 feet above sea level. you see ship a, and your eyes make an angle of 60° with the ship. then you see ship b, which is 1,000sqrt3 feet beyond ship a. the angle of depression that your eyes make with ship b is ? °. a. 30 b. 45 c. 60 d. 90

option A. 30 °.

Explanation:

1) Draw this triangle: Eyes - Ship A - height of the cliff:

The angle of the vertix where the eyes are is: 90° - depreesion angle = 90° - 60° = 30°.

2) opossite leg = horizontal distance to the ship A = x

3) adjacent leg = height of the cliff = 1500 feet

4) tan(30°) = x / 1500 feet => x = 1500 tan(30°) = 1500 √3 / 3 = 500√3

5) Draw the triangle of the eyes - ship B - hieght of the cliff

6) The unknown is the depression angle of the eyes with ship B, α

7) opposite leg = 500√3 feet + 1000√3 feet = 1500√3 feet

8) adjacent leg = height of the cliff = 1500 feet

9) tan(α) = opposite leg / adjacent leg = 1500√3 / 1500 = √3

10) α = arctan(√3) = 60°

11) Depression angle = 90° - 60° = 30° Which is the answer