For this problem we know two angles given 45º and 90º we can fidn the other angle with this operation:
[tex]<3=180º-90º-45º=45º[/tex]
And we know one size who represent the hypothenuse given by:
[tex]7\sqrt{2}[/tex]
Since we want to find the value of m we can use this formula:
[tex]sin\text{ 45º=}\frac{m}{7\sqrt{2}}[/tex]
And we know that :
[tex]\text{ sin 45=}\frac{\sqrt{2}}{2}=\frac{m}{7\sqrt{2}}[/tex]
And solving for m we got:
[tex]m=\frac{7\sqrt{2}\sqrt{2}}{2}=\frac{7\cdot2}{2}=7[/tex]
The final solution for this case would be m=7
