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 mans feet to the base of the monument is 185√3 feet. the distance from the mans feet to the top of the monument is 370√3 feet. the distance from the mans feet to the base of the monument is 277.5 feet. the distance from the mans feet to the top of the monument is 1,110 feet. the segment representing the monuments height is the longest segment in the triangle.

Explanation:

Step1: Use tangent formula

\(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), where \(\theta = 60^{\circ}\) and opposite is height of monument \(h = 555\) ft. Let distance from man to base be \(d\). So \(\tan60^{\circ}=\sqrt{3}=\frac{555}{d}\), then \(d=\frac{555}{\sqrt{3}} = 185\sqrt{3}\) ft.

Step2: Use Pythagorean theorem for distance to top

Let distance from man to top be \(l\). \(l=\sqrt{555^{2}+(185\sqrt{3})^{2}}=\sqrt{555^{2}+555^{2}}=\sqrt{2\times555^{2}} = 555\sqrt{2}\approx785\) ft.

Answer:

The distance from the man's feet to the base of the monument is \(185\sqrt{3}\) feet. The segment representing the monument's height is the longest segment in the triangle.