Question

A park in a subdivision is triangular-shaped. Two adjacent sides of the park are 573 feet and 536 feet. The angle between the sides is 58 degrees. To the nearest unit, find the area of the park in square yards.

A) 32,557 yd2
B) 14,470 yd2
C) 28,940 yd2
D) 43,410 yd2

Answer 1

Option (b) is correct.

The area of the park is 14,470 square yards.

Explanation:

Given : A park in a subdivision is triangular-shaped. Two adjacent sides of the park are 573 feet and 536 feet. The angle between the sides is 58°.

We have to find the area of the park in square yards.

Since, Given two adjacent sides of the park are 573 feet and 536 feet. The angle between the sides is 58°.

Area of triangle =
`(1)/(2)\cdot a \cdot b\cdot \sin\theta`,

where
`\theta` is the angle between sides a and b.

Substitute, a = 573 , b = 536 and
`\theta=58^(\circ)`

Area of triangle =
`(1)/(2)\cdot 573 \cdot 536 \cdot \sin(58^(\circ))`

Simplify, we have,

Area of triangle =
`130229.66` ft²

Also, 1 feet square = 0.111111 yard square

130229.66 feet square = 14469.96 yard square

Thus, The area of the park is 14,470 square yards.

Answer 2

First, we convert the lengths of the sides from feet to yards:
573 ft = 191 yd
536 ft = 178.7 yd
Area of a triangle is given by:
1/2 absin(C)
A = 1/2 x 191 x 178.7 x sin(58)
A = 14,473 sq yd
The answer is B.