Question

if, in a right triangle, $\theta = 18^{\circ}$ and the side opposite to $\theta$ has length 7, how long is the side adjacent to $\theta$? round to at least 3 decimal places.

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Given \(\theta = 18^{\circ}\) and the opposite side \(=7\). Let the adjacent side be \(x\). Then \(\tan(18^{\circ})=\frac{7}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{7}{\tan(18^{\circ})}\). Since \(\tan(18^{\circ})\approx0.3249\) (a known trigonometric value or can be calculated using a calculator), then \(x = \frac{7}{0.3249}\).

Step3: Calculate the value

\(x=\frac{7}{0.3249}\approx21.545\)

Answer:

\(21.545\)