ANSWER
m = 4
EXPLANATION
If the sine of an angle is the cosine of another angle, this means that the angles are complementary. We can see this in a right triangle:
Since the sum of the interior angles of a triangle is 180º and one of the angles in a right triangle is always 90º, then the sum of the other two angles is 90º:
[tex]\beta=90-\alpha[/tex]
The sine of angle alpha is:
[tex]\sin \alpha=\frac{b}{h}[/tex]
The cosine of angle beta is:
[tex]\cos \beta=\frac{b}{h}[/tex]
We can rewrite this as:
[tex]\cos (90-\alpha)=\frac{b}{h}=\sin \alpha[/tex]
Therefore, for this problem, the angles are complementary angles:
[tex](18m-12)=90-(7m+2)[/tex]
Solving for m:
[tex]\begin{gathered} 18m-12=90-7m-2 \\ 18m+7m=90-2+12 \\ 25m=100 \\ m=\frac{100}{25} \\ m=4 \end{gathered}[/tex]
