Question

which equation can be used to solve for c? a triangle labeled with vertices a, b, c (right - angled at c), side lengths: side opposite to b is b, side ab is c, side bc is 5 in, angle at b is 35°.

Explanation:

Step1: Identify trigonometric ratio

In right triangle $ABC$, angle $B = 35^\circ$, side adjacent to $B$ is 5 in, side $c$ is hypotenuse. Cosine relates adjacent and hypotenuse:
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(35^\circ) = \frac{5}{c}$
Rearrange to solve for $c$:
$c = \frac{5}{\cos(35^\circ)}$

Answer:

$\boldsymbol{c = \frac{5}{\cos(35^\circ)}}$