Question

A triangular lot bounded by three streets has a length of 300 feet on one street, 250 feet on the second, and 420 feet on the third. The smallest angle formed by the streets is 36°. Find the area of the lot.
Options:
A. 22,042 ft^2
B. 30,859 ft^2
C. 37,030 ft^2
D. 33,070 ft^2

Answer 1

Suppose the triangle is labeled ABC. That is, angle A, angle B and angle C. The opposite sides for the respective angles are labeled a, b and c. 

let a = 300, b = 250, c = 420
The smallest angle should correspond to the shortest side. So 36 degrees is angle B. Thus, we have sides a and c, with an included angle B. The area of the triangle is calculated as half of the products of the two sides with sine of the included angle.

Area = (a × c × sinB) / 2
Area = (300 ft × 420 ft × sin36) / 2
Area is 37,030 ft2.

Thus, the answer is letter C.