The measures of M are 50.0 and 130 degrees
The given parameters are:
[tex]\mathbf{m = 5.6cm}[/tex]
[tex]\mathbf{o = 4.6cm}[/tex]
[tex]\mathbf{\angle O = 39^o}[/tex]
The measure of angle M is calculated using the following sine formula
[tex]\mathbf{\frac{o}{sin\ O} = \frac{m}{sin\ M}}[/tex]
So, we have:
[tex]\mathbf{\frac{4.6}{sin\ 39} = \frac{5.6}{sin\ M}}[/tex]
Evaluate sin 39
[tex]\mathbf{\frac{4.6}{0.6293} = \frac{5.6}{sin\ M}}[/tex]
Cross multiply
[tex]\mathbf{sin\ M \times 4.6 = 5.6 \times 0.6293}[/tex]
[tex]\mathbf{sin\ M \times 4.6 = 3.5241}[/tex]
Divide both sides by 4.6
[tex]\mathbf{sin\ M = 0.7661}[/tex]
Take arc sin of both sides
[tex]\mathbf{M = sin^{-1}(0.7661)}[/tex]
[tex]\mathbf{M = 50.0}[/tex]
The other possible value of M is:
[tex]\mathbf{M = 180 -50.0}[/tex]
[tex]\mathbf{M = 130.0}[/tex]
Hence, the measures of M are 50.0 and 130 degrees
Read more about sine equations at:
https://brainly.com/question/14140350
