Question

A triangle has two sides of 30 meters and 26 meters, and the angle between them is an obtuse angle. If the area of the triangle is 300 sq. Meters, find the measure of the obtuse angle (to the nearest degree).

Answer 1

130°

Explanation:

Using the formula

Area of the triangle = 1/2 absin theta

a and b are the sides

theta is the obtuse angle

Given

a = 30m

b = 26m

Area = 200m²

Required

theta

Substitute into the formula;

300 = 1/2(30)*(26)sin theta

300 = 15*26sin theta

300 = 390 sintheta

sin theta = 300/390

sin theta = 10/13

sin theta = 0.7692

theta = arcsin(0.7692)

theta = 50.28degrees

Since the angle is obtuse, it must lie between 90 and 180degrees

theta = 180-50.28

theta = 129.72°

Hence the measure of the obtuse angle to the nearest degree is 130°