Question

use the diagram of the right triangle above and round your answer to the nearest hundredth. if m∠a = 30° and b = 12 meters, find a. a. 17.32 m c. 14 m b. 6.93 m d. 9.99 m please select the best answer from the choices provided

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle (right - angled at \(C\)). We know that \(\tan(A)=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle A = 30^{\circ}\), the opposite side to \(\angle A\) is \(a\) and the adjacent side is \(b = 12\) meters. So \(\tan(30^{\circ})=\frac{a}{b}\).

Step2: Recall the value of \(\tan(30^{\circ})\)

We know that \(\tan(30^{\circ})=\frac{1}{\sqrt{3}}\approx0.577\).

Step3: Solve for \(a\)

From \(\tan(30^{\circ})=\frac{a}{12}\), we can re - arrange the formula to get \(a = 12\times\tan(30^{\circ})\). Substitute \(\tan(30^{\circ})\approx0.577\) into the formula: \(a=12\times\frac{1}{\sqrt{3}}=\frac{12}{\sqrt{3}}\). Rationalize the denominator: \(\frac{12\sqrt{3}}{3} = 4\sqrt{3}\approx4\times1.732 = 6.928\approx6.93\) meters.

Answer:

b. 6.93 m