Question

A triangle has sides of length 5 ft, 9 ft, and 13 ft.

What is the measure of the angle opposite the side that is 9 ft long?
THERE IS NO PIC
30°
41°
60°
87°

Answer 1

See the attached image of what this could look like.
Based on the image
a = 9
b = 5
c = 13
We need to find angle A as its opposite the length of 9 units (a = BC = 9)

Use the law of cosines to find the angle A
a^2 = b^2 + c^2 - 2*b*c*cos(A)
9^2 = 5^2 + 13^2 - 2*5*13*cos(A)
81 = 25 + 169 - 130*cos(A)
81 = 194 - 130*cos(A)
81 - 194 = -130*cos(A)
-113 = -130*cos(A)
-130*cos(A) = -113
130*cos(A) = 113
cos(A) = 113/130
A = arccos(113/130)
A = 29.6306
Rounding to the nearest whole number, the answer is 30 degrees