Question

1. a right triangle with one leg labeled 21, an angle of 52° adjacent to that leg, and the other leg labeled x (the right angle is marked with a red square).

Explanation:

Step1: Identify trigonometric ratio

For the 52° angle, the side of length 21 is the adjacent side, and $x$ is the opposite side. Use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(52^\circ)=\frac{x}{21}$

Step3: Solve for $x$

$x=21\times\tan(52^\circ)$
Calculate $\tan(52^\circ)\approx1.2799$, so $x\approx21\times1.2799$

Answer:

$x\approx26.88$