Question

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

Explanation:

Step1: Identify trigonometric ratio

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. In the right - triangle, the angle $\theta = 15^{\circ}$, the opposite side to the angle is 16 and the hypotenuse is $b$. So, $\sin15^{\circ}=\frac{16}{b}$.

Step2: Solve for $b$

We can re - arrange the equation $\sin15^{\circ}=\frac{16}{b}$ to get $b=\frac{16}{\sin15^{\circ}}$.
We know that $\sin15^{\circ}=\sin(45^{\circ}- 30^{\circ})=\sin45^{\circ}\cos30^{\circ}-\cos45^{\circ}\sin30^{\circ}=\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}\times\frac{1}{2}=\frac{\sqrt{6}-\sqrt{2}}{4}\approx0.2588$.
Then $b = \frac{16}{0.2588}\approx61.79$.

Answer:

$61.79$