Question

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

Explanation:

Step1: Identify the trigonometric ratio

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 68^{\circ}$, the opposite - side to the angle $\theta$ is $a$ and the hypotenuse is $16$. So, $\sin68^{\circ}=\frac{a}{16}$.

Step2: Solve for $a$

Multiply both sides of the equation $\sin68^{\circ}=\frac{a}{16}$ by $16$. We get $a = 16\times\sin68^{\circ}$.
Since $\sin68^{\circ}\approx0.9272$, then $a = 16\times0.9272=14.8352$.

Step3: Round the answer

Rounding $14.8352$ to two decimal places, we get $a\approx14.84$.

Answer:

$14.84$