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?

## 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

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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:

24

^{2}=12^{2}+x^{2}576=144+x

^{2}576-144=x

^{2}432=x

^{2}x=20.7846 inches

x=20.8 inches to the nearest tenth