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)
Responses
240 inches
240 inches
66 feet
66 feet
55 feet
55 feet
680 inches
680 inches
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To solve this problem, we can set up a right triangle with the tree's height as the opposite side, the distance from Shaina to the tree as the adjacent side, and Shaina's height as the opposite side.
Given that Shaina's height is 5 feet 6 inches, we convert this to inches: 5 feet * 12 inches/foot + 6 inches = 66 inches.
Now, using the trigonometric ratio for tangent (opposite/adjacent) we have:
tan(68 degrees) = height of tree / 20 feet
tan(68 degrees) = height of tree / 240 inches
height of tree = 240 inches * tan(68 degrees)
height of tree ≈ 680 inches
Therefore, the height of the tree is approximately 680 inches. So the answer is:
680 inches.