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If $\sin (A + 2B) = 2 \cos 60^\circ$ and $A = 3B$, find the measures of $A$ and $B$.
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$\sin (A + 2B) = 1$ (1/2 Mark)
$A + 2B = 90^\circ$ (1/2 Mark)
Using $A = 3B$, we get
$B = 18^\circ$ (1/2 Mark)
$A = 54^\circ$ (1/2 Mark)
$A + 2B = 90^\circ$ (1/2 Mark)
Using $A = 3B$, we get
$B = 18^\circ$ (1/2 Mark)
$A = 54^\circ$ (1/2 Mark)