Law of Sines Basic Application In , given , , and , find .

Trigonometry Solution – Problem 21: find

Law of Sines Basic Application

In $\triangle ABC$ , given $b = 2$ , $B = 30°$ , and $C = 45°$ , find $c$ .

Using the Law of Sines:

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

$\frac{2}{\sin 30°} = \frac{c}{\sin 45°}$

$\frac{2}{\frac{1}{2}} = \frac{c}{\frac{\sqrt{2}}{2}}$

$4 = \frac{2c}{\sqrt{2}}$

$c = 2\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 2$

$2$

Choose the correct theorem (2 pts): Law of Sines / Law of Cosines / area formula / circumradius relation as appropriate.
Set up equations correctly (2 pts): substitute given data and write a solvable system.
Solve and (if needed) reject extraneous cases (2 pts): handle SSA ambiguity or inequality constraints if present.
Final answer (1 pt): provide the requested length/angle/area in the required form.