ANSWER
A. M = 38.2°, n = 159, p = 202
EXPLANATION
We know that the measures of the two non-right interior angles of a right triangle add up to 90°, so knowing that the measure of angle N is 51.8°, we can find the measure of angle M,
[tex]M+N=90\degree[/tex]
Solving for M,
[tex]M=90\degree-N=90\degree-51.8\degree=38.2\degree[/tex]
Hence, the measure of angle M is 38.2°.
To find n, which is the length of the opposite side to angle N, since we know the length of the adjacent side, we can use the tangent of angle N,
[tex]\tan51.8\degree=\frac{n}{125}[/tex]
Solving for n,
[tex]n=125\tan51.8\degree\approx159[/tex]
Hence, n = 159, rounded to three significant digits.
For p, we will use the cosine of angle N,
[tex]\cos51.8\degree=\frac{125}{p}[/tex]
Solving for p,
[tex]p=\frac{125}{\cos51.8\degree}\approx202[/tex]
Hence, p = 202, rounded to three significant digits.
