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The brace for a certain type of mailbox forms a 30°-60°-90° triangle with the side opposite the 30° angle 12 inches in length. What is the length of the side o

The brace for a certain type of mailbox forms a 30°-60°-90° triangle with the side opposite the 30° angle 12 inches in length. What is the length of the side opposite the 60° angle in the triangle to the nearest tenth?
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1 Answer

In a 30-60-90 right triangle, the side opposite the 30º angle is half the measure of the hypotenuse.
Let x=the length of the side opposite the 60º angle.
The hypotenuse has a measure of 24 inches and the leg opposite the 30º angle has a measure of 12 inches.
Using the Pythagorean Theorem:
242=122+x2
576=144+x2
576-144=x2
432=x2
x=20.7846 inches
x=20.8 inches to the nearest tenth