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 trigonometric ratio

In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite leg to the length of the adjacent leg. So, \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 30^{\circ}\), adjacent leg \(= 25\) inches, and we need to find the opposite leg (let's call it \(x\)).

Step2: Substitute values into the formula

We know that \(\tan(30^{\circ})=\frac{x}{25}\). The value of \(\tan(30^{\circ})=\frac{1}{\sqrt{3}}\approx0.577\). So, we can rewrite the equation as \(x = 25\times\tan(30^{\circ})\).

Step3: Calculate the value

Substitute \(\tan(30^{\circ})\approx0.577\) into the equation: \(x = 25\times0.577 = 14.425\approx14.4\) (rounded to the nearest tenth).

Answer:

14.4 in.