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°

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 °