Question

Solve triangle QRS with the given parts. q = 9.10, r = 18.2, Q = 30.0°

Answer 1

Given:

q = 9.10, r = 18.2, Q = 30 degrees

Required: Solve triangle QRS

Explanation:

By using the Sine rule,

$\frac{\sin Q}{q}=\frac{\sin R}{r}=\frac{\sin S}{s}$

Plug the given values.

$\frac{\sin30\degree}{9.10}=\frac{\sin R}{18.2}=\frac{\sin S}{s}$

Consider

$\frac{\sin30\degree}{9.10}=\frac{\sin R}{18.2}$

Solve for R.

$\begin{gathered} \frac{0.5}{9.10}=\frac{\sin R}{18.2} \\ \sin R=\frac{0.5\times18.2}{9.10} \\ =1 \\ \implies R=90\degree \end{gathered}$

Now, use the fact that the sum of the interiorn angles od a r