#### Answer

$n=154$ m
$p= 198$ m
$M=38.8^{\circ}$

#### Work Step by Step

Step 1: To find $n$, we use the formula $\tan\theta=\frac{n}{m}$.
Step 2: $\tan51.2^{\circ}=\frac{n}{124}$
Step 3: $n=124\times\tan51.2^{\circ}$
Step 4: Using a calculator, $n\approx154.2$
Step 5: Rounding the answer to three significant degrees, $n\approx154$ m.
Step 6: To find $p$, we use the formula $\cos\theta=\frac{m}{p}$.
Step 7: $\cos51.2^{\circ}=\frac{124}{p}$
Step 8: $p=\frac{124}{\cos51.2^{\circ}}$
Step 9: Using a calculator, $p\approx197.9$
Step 10: Rounding the answer to three significant degrees, $p\approx198$ m.
Step 11: As $M+N=90^{\circ}$,
$M=90^{\circ}-51.2^{\circ}$
Step 12: Solving, $M=38.8^{\circ}$.