Chapter 10.6, Problem 2STP

Solve each exercise and enter your answer on the grid provided.

A right triangle’s hypotenuse is 20 cm long. What is the length of the side opposite a 60° angle? Give your answer to the nearest tenth of a centimeter.

To determine

To find the length of a side opposite to $60°$ angle in a right triangle.

Answer to Problem 2STP

  

Explanation of Solution

Given information:

Hypotenuse is 20 cm long.

Formula used:

Law of sines.

In any triangle, the ratio of side length to the sine of its opposite angle is the same for all three sides.

Calculation :

Consider x cm be the length of the side opposite to $60°$ angle.

  $\begin{array}{l}\frac{x}{\sin 60}=\frac{20}{\sin 90}\left[\text{opposite angle of hypotenuse is always 90}°\right]\\ \frac{x}{0.866}=\frac{20}{1}\left[\sin 90=1,\sin 60=0.866\right]\\ 20\cdot \left(0.866\right)=x\left[\text{cross multiplication}\right]\\ x=17.3\end{array}$

The length of the side opposite to $60°$ angle is 17.3 cm.