Question

use a trigonometric ratio to solve for a. round to two decimal places as necessary. 25 61° a show your work here a =

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, we know the adjacent side to the given angle and we want to find the opposite side. We use the tangent ratio. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 61^{\circ}$, the adjacent side is 25, and the opposite side is $a$. So, $\tan(61^{\circ})=\frac{a}{25}$.

Step2: Solve for $a$

We can rewrite the equation as $a = 25\times\tan(61^{\circ})$. Since $\tan(61^{\circ})\approx1.804047755$, then $a=25\times1.804047755$.

Step3: Calculate and round

$a = 45.101193875\approx45.10$.

Answer:

$45.10$