Question

use a trigonometric ratio to solve for a. round to two decimal places as necessary. draw right triangle with angle 52°, adjacent side 27, opposite side a

Explanation:

Step1: Identify trigonometric ratio

For the $52^\circ$ angle, the side of length 27 is the adjacent side, and $a$ is the opposite side. Use the tangent ratio: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(52^\circ)=\frac{a}{27}$

Step3: Solve for $a$

Rearrange to isolate $a$: $a=27\times\tan(52^\circ)$
Calculate $\tan(52^\circ)\approx1.2799$, so $a\approx27\times1.2799$

Step4: Compute final value

$a\approx34.56$

Answer:

$34.56$