High Cliff Question

Question

1. An observer stands on the edge of a 375 m high cliff. Below him is a river. He estimates that the angle of depression to the near bank of the river is 80° and the angle of depression to the far bank is 60°. Find the width of the river to the nearest meter. (4 marks)

Answer 1

I assume this is right triangle trig and not LOS or LOC. We can find the length of the base of both right triangles and subtract the smaller from the larger.

The first right triangle has an angle measure of 80 deg. since angle of depression = angle of elevation. The opposite side is 375'. To find the base, use tan(80) = 375/x so x = 66.123 ft.

The larger right triangle has an angle measure of 60 deg. since angle of depression = angle of elevation. The opposite side is 375'. To find the base, use tan(60) = 375/y so y = 216.506 ft. This includes the value of x so to find the width of the river, subtract x from y and you get 150.383 ft.