Question

if, in a right triangle, $\theta = 14^{circ}$ and hypotenuse has length 5, how long is the side opposite to $\theta$? round to at least 3 decimal places.

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Let the side opposite to \(\theta\) be \(x\), hypotenuse \(c = 5\), and \(\theta=14^{\circ}\). So, \(\sin(14^{\circ})=\frac{x}{5}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(14^{\circ})=\frac{x}{5}\) by \(5\). We get \(x = 5\times\sin(14^{\circ})\).
Since \(\sin(14^{\circ})\approx0.24192\) (using a calculator in degree mode), then \(x=5\times0.24192 = 1.2096\).

Answer:

\(1.210\)