A triangle has angles that measure 30o, 60o, and 90o. The hypotenuse of the triangle measures 10 inches. Which is the best estim
ate for the perimeter of the triangle? Round to the nearest tenth.
2 answers:
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.
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