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

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

Step2: Rearrange for hypotenuse

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

Step3: Substitute given values

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

Step4: Calculate value

$\sin(80^\circ) \approx 0.9848$, so $\text{hypotenuse} \approx \frac{4}{0.9848} \approx 4.06$

Step5: Round to nearest tenth

$4.06 \approx 4.1$

Answer:

4.1 in.