Question

solve for y to the nearest hundredth.
image of a right triangle with one leg labeled 12, one leg labeled y, hypotenuse labeled x, and an angle of 30° between the leg of length 12 and the hypotenuse

Explanation:

Step1: Identify trigonometric ratio

In the right triangle, we have a 30° angle, adjacent side (to 30°) is 12, and opposite side is \( y \). We use the tangent function: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So \( \tan(30^\circ)=\frac{y}{12} \).

Step2: Solve for \( y \)

We know \( \tan(30^\circ)=\frac{1}{\sqrt{3}}\approx0.5774 \). Multiply both sides by 12: \( y = 12\times\tan(30^\circ) \). Substitute the value: \( y = 12\times\frac{1}{\sqrt{3}} = 4\sqrt{3}\approx6.93 \).

Answer:

\( 6.93 \)