Question

in a right triangle, angle a measures 20°. the side opposite angle a is 10 centimeters long. approximately how long is the hypotenuse of the triangle? 27.5 centimeters 3.4 centimeters 29.2 centimeters 10.6 centimeters

Explanation:

Step1: Recall sine formula

In a right - triangle, $\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}$. Let the hypotenuse be $c$. We know that $A = 20^{\circ}$ and the side opposite to angle $A$ is $a = 10$ cm. So, $\sin(20^{\circ})=\frac{10}{c}$.

Step2: Solve for hypotenuse

We can re - arrange the formula to get $c=\frac{10}{\sin(20^{\circ})}$. Since $\sin(20^{\circ})\approx0.342$, then $c=\frac{10}{0.342}\approx29.2$ cm.

Answer:

29.2 centimeters