Question

Solve the right triangle. Round off the results according to the table below.

Answer 1

A. M = 38.2°, n = 159, p = 202

Step-by-step 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,

`M+N=90\degree`

Solving for M,

`M=90\degree-N=90\degree-51.8\degree=38.2\degree`

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,

`\tan51.8\degree=(n)/(125)`

Solving for n,

`n=125\tan51.8\degree\approx159`

Hence, n = 159, rounded to three significant digits.

For p, we will use the cosine of angle N,

`\cos51.8\degree=(125)/(p)`

Solving for p,

`p=(125)/(\cos51.8\degree)\approx202`

Hence, p = 202, rounded to three significant digits.