Find θ if d is 2.6 miles. Round to the nearest tenth.

Question

The radar on a ship picks up two shipwrecks, A and B, 5.12 miles beneath the surface. The distance between the shipwrecks is 1.25 miles. The angle of depression to Shipwreck B depends on the horizontal distance, d, from the ship to Shipwreck A.

Find θ if d is 2.6 miles. Round to the nearest tenth.

Write only your numeric answer.

Answer 1

S------------------------------------

| * θ

| *

| *

| *

|______ __ A___*B__________

F 2.6 1.25

Without a diagram, I can only speculate on the geometry. The diagram above is my interpretation of the problem. The dashed line represent the water surface. The solid line below is the sea floor. The asterisks represent a straight line from the ship S to wreck B. Triangle SFB is a right triangle. The angle SFB is

arctan (2.6 + 1.25) / 5.12= 36.9 degrees. The angle of depression θ is 90 - 36.9 = 53.1 degrees. Round to 2 sig figs.