Question

unit exam - right triangles and trigonometry
solve for c.
b = 15
c = ?
law of sines: $\frac{sin a}{a} = \frac{sin b}{b} = \frac{sin c}{c}$
round your answer to the nearest hundredth.

Explanation:

Step1: Calculate angle A

The sum of angles in a triangle is $180^\circ$.
$\angle A = 180^\circ - 125^\circ - 20^\circ = 35^\circ$

Step2: Apply Law of Sines

Relate side $b$, angle $A$, side $c$, angle $C$.
$\frac{\sin A}{b} = \frac{\sin C}{c}$

Step3: Rearrange to solve for c

Isolate $c$ using cross-multiplication.
$c = \frac{b \cdot \sin C}{\sin A}$

Step4: Substitute values and compute

Plug in $b=15$, $\sin35^\circ\approx0.5736$, $\sin20^\circ\approx0.3420$.
$c = \frac{15 \cdot \sin20^\circ}{\sin35^\circ} \approx \frac{15 \cdot 0.3420}{0.5736} \approx \frac{5.13}{0.5736} \approx 8.94$

Answer:

$8.94$