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. 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 feet. The distance from the man’s feet to the top of the monument is 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

I have tried solving the problem, and none of the values in the choices matched with mine.

Illustrating the problem, it shows a right triangle, one angle is 60° with the opposite vertical side measuring 555 ft which is the height of the monument. Using the pythagorean theorem, the distance between the man's feet to the top of the monument being the hypotenuse (longest side), the hypotenuse would be 640.86 ft and the distance from the man's feet to the monument's base is 320.43 ft.

sin 60 = 555/hypotenuse
hypotenuse = 640.86 ft

tan 60 = 555/base
base = 320.43 ft

Answer 2

The distance between the man's feet to the top of the monument is 640.858 ft and the distance between the man's feet to the base of the monument is 320.42 ft and this can be determine by using the trignometry function.

Given :

60° angle of elevation from the ground.

Height of the monument = 555 ft.

To determine the distance between the men and the monument that is base, trignometry function can be use.

$\rm sin\theta = \dfrac{Perpendicular}{Hypotenuse}$

$\rm sin60^\circ=\dfrac{555}{Hypotenuse}$

$\rm \dfrac{\sqrt{3} }{2}=\dfrac{555}{Hypotenuse}$

Hypotenuse = 640.858 ft.

Therefore, the distance between the man's feet to the top of the monument is 640.858 ft.

$\rm cos 60^\circ = \dfrac{Base}{Hypotenuse}$

$\rm \dfrac{1}{2}=\dfrac{Base}{640.858}$

Base = 320.42 ft.

Therefore, the distance between the man's feet to the base of the monument is 320.42 ft.

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