10
QuizMultiple Choice

Similar Triangles

Question 10 • Mathematical Models with Applications - MA4072 CR

You and a friend want to know how much rope you need to climb a large rock. Your friend is 5.5 feet tall and casts a shadow that is 18 feet long. If the rock casts a shadow that is 209.5 feet long, calculate the height of the rock from the ground. Round your answer to the nearest foot. (Hint: make a drawing)

Answer
A
64 ft
B
18 ft
C
210 ft
D
219 ft

Explanation

The friend and the rock form similar triangles because sunlight creates the same angle for both shadows. Set up the proportion 5.5/18 = h/209.5. Solving gives h = (5.5 × 209.5)/18 ≈ 64.0 feet, so the rock is about 64 feet tall. The correct choice is 64 ft.

AI-written and checked against the verified answer.

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