Question

if, in a right triangle, $\theta = 12^{\circ}$ and the side adjacent to $\theta$ has length 3, how long is the side opposite $\theta$? round to 3 decimal places.

Explanation:

Step1: Recall the tangent function formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Given \(\theta = 12^{\circ}\) and adjacent \(=3\). Let the opposite side be \(x\). Then \(\tan(12^{\circ})=\frac{x}{3}\).

Step2: Solve for \(x\)

We know that \(x = 3\times\tan(12^{\circ})\). Using a calculator, \(\tan(12^{\circ})\approx0.2125565617\). Then \(x=3\times0.2125565617\).

Step3: Calculate the value of \(x\)

\(x = 0.6376696851\approx0.638\)

Answer:

\(0.638\)