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? Round to the nearest degree. 30° 41° 60° 87°

Answer 1

30°

Proof in pic:

Answer 2

Using cosine theorem we have:
9 ^ 2 = 5 ^ 2 + 13 ^ 2 -2 * 5 * 13 * cos (x)
Clearing the angle we have:
cos (x) = ((9 ^ 2) - (5 ^ 2) - (13 ^ 2)) / (- 2 * 5 * 13)
cos (x) = 0.869230769
x = acos (0.869230769)
x = 29.63062742 degrees
Round to the nearest degree:
x = 30 degrees
Answer:
the measure of the angle opposite the side that is 9 ft long is:
30 °