Question

Use trigonometric ratios to solve the following problem. Shaina, who is 5 feet, 6 inches tall, is standing 20 feet from the base of a tree when she sees a pileated woodpecker at the top of the tree. The bird is at an angle of elevation of 68 degrees above Shaina’s line of sight. What is the height of the tree?

(1 point)
Responses

55 feet
55 feet

240 inches
240 inches

680 inches
680 inches

66 feet

Answer 1

Let Shaina’s eye height = 5 ft 6 in = 5.5 ft. With angle of elevation 68° and horizontal distance 20 ft, the bird’s height above her eyes is

height_above_eyes = 20 · tan(68°) ≈ 20 · 2.475 ≈ 49.5 ft.

Total tree height = 5.5 + 49.5 = 55.0 ft.

Answer: 55 feet.