Question

In the given problem solve the triangle using either the law of sines or law of cosines-

$B=35°,C=65°,a=15$

Short answer

Required values of the triangle are,

$b\approx 13.2,c\approx 13.5,A=80°$

Step-by-step solution

Step 1. Given information

In the given triangle,

$B=35°,C=65°,a=15$

We know Law of sines,

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Step 2. Calculation

We know, sum of all angles of a triangle i.e.

$$\begin{gathered} A+B+C=180° \\ \Rightarrow A+35°+65°=180° \\ \Rightarrow A=180°-100° \\ \Rightarrow A=80° \end{gathered}$$

For side $b$,

$\frac{\sin A}{a}=\frac{\sin B}{b}$

$$\begin{gathered} \Rightarrow \frac{\sin 80°}{15}=\frac{\sin 35°}{b} \\ \Rightarrow b=\frac{0.57}{0.98}\times 15 \\ \Rightarrow b\approx 13.2 \end{gathered}$$

For side $c$,

$$\begin{gathered} \frac{\sin A}{a}=\frac{\sin C}{c} \\ \Rightarrow \frac{\sin 80°}{15}=\frac{\sin 65°}{c} \\ \Rightarrow c=\frac{0.9}{0.98}\times 15 \\ \Rightarrow c\approx 13.5 \end{gathered}$$