Question

A man is standing near the Washington Monument. At a 60° angle of elevation from the ground, the man sees the top of the 555-foot monument.

A man is standing near the Washington Monument to form a triangle. The height of the monument is 555 feet. The angle where the man is standing is 60 degrees. The monument and the ground form a right angle.

Which measurements are accurate based on the scenario? Check all that apply.

The distance from the man’s feet to the base of the monument is 185 StartRoot 3 EndRoot feet.
The distance from the man’s feet to the top of the monument is 370 StartRoot 3 EndRoot feet.
The distance from the man’s feet to the top of the monument is 1,110 feet.
The distance from the man’s feet to the base of the monument is 277.5 feet.
The segment representing the monument’s height is the longest segment in the triangle.

Answer 1

Correct choices:
- The distance from the man’s feet to the base of the monument is 185√3 feet.
- The distance from the man’s feet to the top of the monument is 370√3 feet.

Work:
- Let x = horizontal distance from man to base. tan 60° = √3 = opposite/adjacent = 555/x → x = 555/√3 = 185√3 ≈ 320.43 ft.
- Hypotenuse h: sin 60° = (√3/2) = 555/h → h = 555/(√3/2) = 1110/√3 = 370√3 ≈ 640.85 ft.

Therefore the 1110 ft and 277.5 ft options are incorrect, and the monument’s height (555 ft) is not the longest segment (the hypotenuse ≈ 640.85 ft is longest).