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 sine definition

In a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Rearrange for hypotenuse

$\text{hypotenuse} = \frac{\text{opposite side}}{\sin(\theta)}$

Step3: Substitute given values

$\text{hypotenuse} = \frac{4}{\sin(80^\circ)}$

Step4: Calculate and round

$\sin(80^\circ) \approx 0.9848$, so $\text{hypotenuse} \approx \frac{4}{0.9848} \approx 4.1$

Answer:

4.1 in.