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 °
