Question

find the length of side c.
b
c
a
a
50°
35°
c
13
b = 95°
a = 10.0
c = ?

Explanation:

Step1: Identify the Law of Sines

We use the Law of Sines, which states that $\frac{a}{\sin A}=\frac{c}{\sin C}$.

Step2: Plug in the known values

We know $a = 10.0$, $A = 95^\circ$, $C = 35^\circ$. So we have $\frac{10.0}{\sin 95^\circ}=\frac{c}{\sin 35^\circ}$.

Step3: Solve for c

First, find $\sin 95^\circ\approx0.9962$ and $\sin 35^\circ\approx0.5736$. Then, $c=\frac{10.0\times\sin 35^\circ}{\sin 95^\circ}=\frac{10.0\times0.5736}{0.9962}\approx5.76$.

Answer:

Approximately 5.76