Question

Reed is snorkeling on the surface of the ocean, 22 feet from an anchored boat. The anchor is on the ocean floor, 34 feet away from Reed. What is the angle of depression between Reed and the anchor?(1 point)
Responses

50°
50
°

50 degrees

65°
65
°

65 degrees

90°
90
°

90 degrees

40°

Answer 1

Let the vertical depth be h. In the right triangle with horizontal 22 and hypotenuse 34,
h = sqrt(34^2 − 22^2) = sqrt(1156 − 484) = sqrt(672) ≈ 25.92 ft.
Angle of depression θ satisfies tan θ = opposite/adjacent = h/22 ≈ 25.92/22 ≈ 1.178,
so θ = arctan(1.178) ≈ 50°.

Answer: 50°.