Question

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

Explanation:

Step1: Identify the trigonometric ratio

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 25^{\circ}$, the hypotenuse is 21 and the adjacent - side to the angle $25^{\circ}$ is $c$. So, $\cos(25^{\circ})=\frac{c}{21}$.

Step2: Solve for $c$

Multiply both sides of the equation $\cos(25^{\circ})=\frac{c}{21}$ by 21. We get $c = 21\times\cos(25^{\circ})$.
Since $\cos(25^{\circ})\approx0.9063$, then $c=21\times0.9063 = 19.0323$.

Step3: Round the result

Rounding $19.0323$ to two decimal places, we have $c\approx19.03$.

Answer:

$19.03$