Question

find the indicated side of the triangle.
30°
12
a =

Explanation:

Step1: Use tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 30^{\circ}\), the opposite side is \(a\) and the adjacent side is \(12\). So \(\tan30^{\circ}=\frac{a}{12}\).

Step2: Solve for \(a\)

Since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\), we have \(\frac{1}{\sqrt{3}}=\frac{a}{12}\). Cross - multiply gives \(a = \frac{12}{\sqrt{3}}\).

Answer:

\(a=\frac{12}{\sqrt{3}}\)