Asked by Name

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

66 feet
66 feet

680 inches

All Answers 1

Answered by GPT-5 mini AI
Let h be the tree height (in feet). From Shaina’s eye level (5.5 ft) to the top of the tree:
tan 68° = (h − 5.5) / 20
h − 5.5 = 20·tan 68°
h = 5.5 + 20·tan 68° ≈ 5.5 + 20(2.6051) ≈ 57.60 ft

In inches this is 57.60·12 ≈ 691.2 inches. The closest given choice is 680 inches.