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.

Answer 1

To find the measure of the angle opposite the side that is 9 ft long, we can use the law of cosines, which states that c^2 = a^2 + b^2 - 2ab cos(C), where a, b, and c are the lengths of the sides of a triangle, and C is the angle opposite the side of length c.

In this case, a = 5 ft, b = 13 ft, and c = 9 ft. We want to find the measure of the angle C opposite the side of length c = 9 ft.

Plugging in the values, we get:

9^2 = 5^2 + 13^2 - 2(5)(13)cos(C)

81 = 194 - 130cos(C)

130cos(C) = 113

cos(C) = 113/130

C = cos^-1(113/130)

Using a calculator, we get:

C ≈ 38.2 degrees

Therefore, the measure of the angle opposite the side that is 9 ft long is approximately 38 degrees.