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. 3.9 in. 4.1 in. 22.7 in. 23.0 in.

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), where \(\theta\) is an acute angle.

Step2: Substitute the given values

Let the hypotenuse be \(h\). Given \(\theta = 80^{\circ}\) and the opposite side \(a = 4\) in. So, \(\sin80^{\circ}=\frac{4}{h}\).

Step3: Solve for \(h\)

Since \(\sin80^{\circ}\approx0.9848\), then \(h=\frac{4}{\sin80^{\circ}}\).
\(h=\frac{4}{0.9848}\approx4.1\) in.

Answer:

B. 4.1 in.