Question

2)
in a right triangle, the hypotenuse is 10, one acute angle is 63°, find the length of the side labeled x adjacent to the 63° angle.

Explanation:

Step1: Identify trigonometric ratio

For the 63° angle, $x$ is opposite, hypotenuse = 10. Use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(63^\circ)=\frac{x}{10}$

Step2: Solve for $x$

Rearrange to isolate $x$: $x = 10\times\sin(63^\circ)$
Calculate $\sin(63^\circ)\approx0.8910$, so $x\approx10\times0.8910$

Answer:

$x\approx8.91$