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.
