Answer:
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°