39
QuizMultiple Choice

Cumulative Exam — Cumulative exam

Question 39 • AL-Algebra II with Statistics

A tree is leaning at a 5° angle from vertical, making an 85° angle with the ground. When the sun is at a 65° angle of elevation, the tree casts a 25-foot shadow. What is the approximate length of the tree?

Answer
A
23 ft.
B
27 ft.
C
45 ft.
D
50 ft.

Explanation

The triangle is formed by the tree, its 25-foot shadow, and the sun’s ray. Its angles are 85° where the tree meets the ground and 65° where the ray meets the ground, so the third angle is 30°. By the sine rule, the tree’s length is 25 × sin(65°) ÷ sin(30°) ≈ 45 feet, so the correct choice is 45 ft.

AI-written and checked against the verified answer.

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