Question

A park in a subdivision has a triangular shape two adjacent side of the park are 433 and 520 the angle between the sides is 37 find the area of the park to the nearest square foot hint use theorem 10-8

Answer 1

Answer:

$67750.644 ft^2$

Step-by-step explanation:

Given : A park in a subdivision has a triangular shape two adjacent side of the park are 433 and 520 the angle between the sides is 37

To Find: the area of the park to the nearest square foot

Solution:

Refer the attached figure

Area of triangle = $\frac{1}{2} \times a \times b \times sin c$

a = 433

b=520

Sin c = Sin 37° = 0.6018

Area of triangle = $\frac{1}{2} \times 433 \times 520 \times 0.6018$

Area of triangle = $67750.644$

Hence the area of the park is $67750.644 ft^2$

Answer 2

See attached graphic.
area = .5 * side1 * sine (included angle) * side2
area = .5 * 433 * sine (37 degrees) * 520
area = .5 * 433 * 0.60182 * 520
area = 67,753 square feet

Source:
http://www.1728.org/triang.htm