Question

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.

Answer 1

Given: In Δ ABC, ∠B =90° , ∠C = 30° , ∠A = 60° and Hypotenuse AC = 10 inches

It has been described in the attachment.

Now, we shall calculate side AB and BC by using Trigonometric Ratios.

Sin 30° = AB / AC

or,     AB = 10 × Sin 30° = 10 × 0.5 = 5 inches

And,  Cos 30° = CB / AC

or,               CB =  10 × Cos 30° = 10 × 0.866 = 8.66 inches

Now, we shall calculate the perimeter of the given triangle

Perimeter of the triangle = AB + BC + CA

or,                                      = (5.0 + 8.66 + 10.0 ) inches

or,                                      = 23.66 inches ≈ 23.7 inches

Hence, the best estimate for the perimeter of the triangle ( round to the nearest tenth will be 23.7 inches.

Answer 2

Answer: 23.7

Step-by-step explanation: it’s right