Question

in a 30° - 60° - 90° triangle, if the hypotenuse is 9 inches, find the side opposite the 30° angle. round your answer to the tenths place. question 5 1 pts in a 30° - 60° - 90° triangle, if the hypotenuse is 9 inches, find the side opposite the 60° angle. round your answer to the tenths place.

Explanation:

Step1: Recall the properties of a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle

In a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle, if the hypotenuse \(c = 9\) inches, the side opposite the \(30^{\circ}\) angle \(a=\frac{c}{2}\), and the side opposite the \(60^{\circ}\) angle \(b = \frac{\sqrt{3}}{2}c\).

Step2: Calculate the side opposite the \(30^{\circ}\) angle

For the side opposite \(30^{\circ}\): \(a=\frac{9}{2}=4.5\) inches.

Step3: Calculate the side opposite the \(60^{\circ}\) angle

For the side opposite \(60^{\circ}\): \(b=\frac{\sqrt{3}}{2}\times9=\frac{9\sqrt{3}}{2}\approx\frac{9\times1.732}{2}=\frac{15.588}{2}=7.8\) inches.

Answer:

The side opposite the \(30^{\circ}\) angle is \(4.5\) inches. The side opposite the \(60^{\circ}\) angle is \(7.8\) inches.