Question

find the value of x for the right triangle.
30°
13
x
x = \square

Explanation:

Step1: Identify trigonometric ratio

In a right triangle, for a 30° angle, the side opposite (x) and hypotenuse (13) relate via sine: $\sin(30^\circ) = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Substitute values

$\sin(30^\circ) = \frac{1}{2}$, so $\frac{1}{2} = \frac{x}{13}$.

Step3: Solve for x

Multiply both sides by 13: $x = 13 \times \frac{1}{2} = \frac{13}{2} = 6.5$.

Answer:

$6.5$ (or $\frac{13}{2}$)