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.

Answer 1

The perimeter of the park is 1466 feet

Step-by-step explanation:

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°

We need to find the perimeter of the park

∵ The city park is rectangular in shape

∵ The longer side of the park is 500 feet

∵ The angle formed by the walkway and the shorter side of

   the park is 65°

The longer side, the shorter side of the park and the walkway formed a right triangle, with longer side opposite to the angle of measure 65° and the shorter side adjacent to it, so we can use the trigonometry ratio (tan) to find the length of the shorter side of the park

∵ tan(65) = opposite side/adjacent side

∵ The longer side is the opposite side

∵ The shorter side is the adjacent side

∵ The longer side = 500 feet

∴ $tan(65)=\frac{500}{shorter}$

- By using cross multiplication

∴ tan(65) × shorter side = 500

- Divide both sides by tan(65)

∴ Shorter side = 233.15 feet

∵ The perimeter of a rectangle = 2(length + width)

∴ The perimeter of the park = 2(500 + 233.15)

∴ The perimeter of the park = 2(733.15)

∴ The perimeter of the park = 1466.30 feet

- Rounded it to the nearest foot (to the nearest whole number)

∴ The perimeter of the park = 1466 feet

The perimeter of the park is 1466 feet

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

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