Exercises: Sine and Cosine theorem

Given: $b = 4 cm$ $c = 7.5 cm$ $γ = 108^{\circ}$

Required: $β = ?$

You are given a pair of an angle and a side, as well as the side opposite the angle you are looking for. Therefore you may use the sine theorem.

$\frac{b}{\sin (β)}$	$=$	$\frac{c}{\sin (γ)}$	$\cdot \sin (γ)$
	↓	Hint: By forming the reciprocal value of both fractions, you can get the variable you are looking for into the numerator.
$\frac{\sin (β)}{b}$	$=$	$\frac{\sin (γ)}{c}$	$\cdot b$
	↓	Solve for the required variable.
$\sin (β)$	$=$	$\frac{\sin (γ)}{c} \cdot b$
	↓	Plug in the given values.
$\sin (β)$	$=$	$\frac{\sin (108^{\circ})}{7.5} \cdot 4$
$\sin (β)$	$\approx$	$0.5072$	$\sin^{- 1}$
$β$	$\approx$	$30 .48 °$