A triangle has angles that measure 30o, 60o, and 90o. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle? Round to the nearest tenth. a. 20.0 in. b. 23.1 in. c. 23.7 in. d. 27.4 in.

Answer: c. 23.7 in.

Step-by-step explanation:

From the given right angle triangle,

The hypotenuse of the triangle measures 10 inches.

one of the legs represents the adjacent side of the right angle triangle while the other leg represents the opposite side of the right angle triangle.

We would take 30° as the reference angle. To determine the adjacent side, a we would apply the cosine trigonometric ratio.

Cos θ, = adjacent side/hypotenuse. Therefore,

Cos 30 = a/10

a = 10Cos 30 = 10 * 0.8660

a = 8.66 inches

To determine the opposite side, b we would apply the Sine trigonometric ratio.

Sin θ, = opposite side/hypotenuse. Therefore,

Sin 30 = b/10

b = 10Sin 30 = 10 * 0.5

b = 5 inches

The perimeter of the triangle is

10 + 8.66 + 5 = 23.66 inches

Approximately 23.7 inches