Question

solve for x to the nearest hundredth.
right triangle with right angle at top left, vertical leg length 12, angle at bottom left 30°, hypotenuse labeled x, horizontal leg labeled y

Explanation:

Step1: Identify the trigonometric ratio

In the right triangle, the adjacent side to the 30° angle is 12, and the hypotenuse is \( x \). We use the cosine function, which is defined as \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(30^\circ) = \frac{12}{x} \).

Step2: Solve for \( x \)

Rearrange the formula to solve for \( x \): \( x = \frac{12}{\cos(30^\circ)} \). We know that \( \cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.8660 \). Substitute this value into the formula: \( x = \frac{12}{0.8660} \approx 13.86 \).

Answer:

\( x \approx 13.86 \)