Question

use a trigonometric ratio to solve for a. round to two decimal places as necessary. draw 54° 20 a show your work here a = use a trigonometric ratio to solve for c. round to two decimal places as necessary. draw

Explanation:

Step1: Identify the trigonometric ratio

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In the right - triangle, the angle $\theta = 54^{\circ}$, the opposite side to the angle is $a$ and the adjacent side is 20. So, $\tan(54^{\circ})=\frac{a}{20}$.

Step2: Solve for $a$

Multiply both sides of the equation $\tan(54^{\circ})=\frac{a}{20}$ by 20. We get $a = 20\times\tan(54^{\circ})$. Since $\tan(54^{\circ})\approx1.37638$, then $a=20\times1.37638 = 27.5276$.

Step3: Round the answer

Rounding $27.5276$ to two decimal places, we have $a\approx27.53$.

Answer:

$27.53$