Question

Use the image to answer the question.

A grid shows a right triangle upper A upper B upper C. The angle of the vertex upper B is at the right angle.

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)

66 feet

55 feet

680 inches

240 inches

Answer 1

Let h be the tree height. The vertical distance from Shaina’s eye level to the top is 20·tan(68°). Shaina’s height is 5 ft 6 in = 5.5 ft, so

h = 20·tan(68°) + 5.5 ≈ 20(2.6051) + 5.5 ≈ 52.10 + 5.5 ≈ 57.60 ft.

57.60 ft = 57.60·12 ≈ 691.2 inches. None of the choices match exactly; the closest choice is 680 inches, so select 680 inches.