Originally Posted by
Soroban Hello, magentarita!
If $\displaystyle \sin\alpha \,=\,\cos\beta$, then $\displaystyle \alpha\text{ and }\beta$ are complementary
. . (of both angles are acute angles.)
So we have: .$\displaystyle (2\theta+18) +(5\theta - 12) \:=\:90^o\quad\Rightarrow\quad 7\theta \:=\:84^o \quad\Rightarrow\quad \theta \:=\:12^o$
The two angles are: .$\displaystyle \begin{array}{ccccc}2\theta + 18 &=&2(12) + 18 &=& 42^o \\ 5\theta-12 &=& 5(12) - 12 &=& 48^o \end{array}\quad\hdots $ answer (a)