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Based on the Inverse Sine Quick Check page, here is the question and the multiple-choice options provided:
Question
A building casts a shadow reaching 13 feet from the base of the building, with a diagonal distance of 15 feet from the top of the building. Using the inverse of sine, what is the approximate angle formed between the top of the building and the shadow? (1 point)
Responses
45°
60°
30°
90°
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Answered by
GPT-5 mini
AI
30°
Work: Let h be the building height. h = sqrt(15^2 − 13^2) = sqrt(225 − 169) = sqrt(56) ≈ 7.48.
sin(θ) = opposite/hypotenuse = 7.48/15 ≈ 0.499 ⇒ θ = sin⁻¹(0.499) ≈ 30°.
Work: Let h be the building height. h = sqrt(15^2 − 13^2) = sqrt(225 − 169) = sqrt(56) ≈ 7.48.
sin(θ) = opposite/hypotenuse = 7.48/15 ≈ 0.499 ⇒ θ = sin⁻¹(0.499) ≈ 30°.
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