Question

unit exam - right triangles and trigonometry
solve for c.
a = 34
law of sines: $\frac{sin a}{a} = \frac{sin b}{b} = \frac{sin c}{c}$
round your answer to the nearest hundredth.

Explanation:

Step1: Find angle B

The sum of angles in a triangle is $180^\circ$.
$\angle B = 180^\circ - 70^\circ - 84^\circ = 26^\circ$

Step2: Apply Law of Sines

Relate side $a$, angle $A$, side $c$, angle $C$.
$\frac{\sin A}{a} = \frac{\sin C}{c}$
Substitute values: $\frac{\sin 84^\circ}{34} = \frac{\sin 70^\circ}{c}$

Step3: Rearrange to solve for c

Isolate $c$ using cross-multiplication.
$c = \frac{34 \times \sin 70^\circ}{\sin 84^\circ}$

Step4: Calculate the value

Use trigonometric values ($\sin70^\circ\approx0.9397$, $\sin84^\circ\approx0.9945$).
$c \approx \frac{34 \times 0.9397}{0.9945} \approx \frac{31.9498}{0.9945} \approx 32.13$

Answer:

32.13