Question

a right triangle has a 30° angle. the leg adjacent to the 30° angle measures 25 inches. what is the length of the other leg? round to the nearest tenth. 14.4 in. 21.7 in. 28.9 in. 43.3 in.

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 30^{\circ}\), and the adjacent side \(a = 25\) inches. Let the opposite side (the other leg) be \(x\). So, \(\tan30^{\circ}=\frac{x}{25}\).

Step2: Solve for \(x\)

Since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\approx0.577\), we have \(x = 25\times\tan30^{\circ}\). Substituting the value of \(\tan30^{\circ}\), \(x=25\times\frac{1}{\sqrt{3}}\). Rationalizing the denominator: \(x=\frac{25\sqrt{3}}{3}\).

$$x=\frac{25\times1.732}{3}=\frac{43.3}{3}\approx14.4$$

Answer:

14.4 in.