Question

a right triangle has one side that measures 4 in. the angle opposite that side measures 80°. what is the length of the hypotenuse of the triangle? round to the nearest tenth. 22.7 in. 4.1 in. 3.9 in. 23.0 in.

Explanation:

Step1: Recall sine formula

In a right triangle, \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 80^\circ\), opposite \(= 4\) in, let hypotenuse be \(h\). So \(\sin(80^\circ)=\frac{4}{h}\).

Step2: Solve for \(h\)

Rearrange formula: \(h=\frac{4}{\sin(80^\circ)}\). Calculate \(\sin(80^\circ)\approx0.9848\). Then \(h=\frac{4}{0.9848}\approx4.1\) in.

Answer:

4.1 in