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)

45°

60°

90°

30°

Answer 1

Let θ be the angle between the shadow (ground) and the line from the tip of the shadow to the top of the building. The opposite side (building height) is √(15² − 13²) = √56. So

sin θ = opposite/hypotenuse = √56 / 15 ≈ 0.4989,

θ = sin⁻¹(0.4989) ≈ 30°.

Answer: 30°.