Question

a city park is rectangular in shape. the longer side of the park is 500 feet. a walkway runs diagonally through the park. the angle formed by the walkway and the shorter side of the park is 65°. what is the perimeter of the park? enter your answer, rounded to the nearest foot, in the box. ft

Explanation:

Step1: Find the shorter - side length

Let the longer side $a = 500$ feet and the angle $\theta=65^{\circ}$. We know that $\tan\theta=\frac{a}{b}$, where $b$ is the shorter - side length. So $b=\frac{a}{\tan\theta}$. Substituting $a = 500$ and $\theta = 65^{\circ}$, we have $b=\frac{500}{\tan65^{\circ}}\approx\frac{500}{2.1445}\approx233.15$ feet.

Step2: Calculate the perimeter

The perimeter $P$ of a rectangle is $P = 2(a + b)$. Substituting $a = 500$ and $b\approx233.15$, we get $P=2(500 + 233.15)=2\times733.15 = 1466.3\approx1466$ feet.

Answer:

1466