a man is standing near the washington monument. at a 60° angle of elevation from the ground, the man sees…

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

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

Answer

Explanation:

Step1: Use tangent function for base - distance

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 60^{\circ}$, and the height of the monument (opposite side) is $h = 555$ feet. Let the distance from the man's feet to the base of the monument be $x$. Then $\tan60^{\circ}=\sqrt{3}=\frac{555}{x}$, so $x=\frac{555}{\sqrt{3}}=\frac{555\sqrt{3}}{3}=185\sqrt{3}$ feet.

Step2: Use sine function for distance to the top

Let the distance from the man's feet to the top of the monument be $y$. We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Since $\sin60^{\circ}=\frac{\sqrt{3}}{2}$ and the opposite side is 555 feet, $\sin60^{\circ}=\frac{555}{y}$, so $y=\frac{555}{\sin60^{\circ}}=\frac{555}{\frac{\sqrt{3}}{2}}=\frac{1110}{\sqrt{3}} = 370\sqrt{3}$ feet. Also, in a right - triangle with an angle of $60^{\circ}$, the hypotenuse is the longest side.

Answer:

The distance from the man's feet to the base of the monument is $185\sqrt{3}$ feet. The distance from the man's feet to the top of the monument is $370\sqrt{3}$ feet.