Solve the triangle. Round side measure to the nearest tenth and angle measures to the nearest degree.

First calculate the missing angle [tex]\alpha[/tex]. By knowing all angles in triangle have a sum of 180°.

[tex]\alpha=180-(\gamma+\beta)[/tex]
[tex]\alpha=180-(90+49)=\boxed{41}[/tex]

Now we required to use angle functions in a right triangle. The cosine of [tex]\beta[/tex] is equal to the relation of side [tex]a[/tex] and hypotenuse [tex]c[/tex].

Now we solve this for hypotenuse.

[tex]\cos(\beta)=\frac{a}{c}[/tex]

[tex]c=\frac{a}{\cos(\beta)}[/tex]

Now put in the numbers.

[tex]c=\frac{9}{\cos(49)}\approx\boxed{13.7}[/tex]

So we know the length of hypotenuse and length of side [tex]a[/tex] therefore side [tex]b[/tex] can be calculated using Pythagorean theorem: [tex]c^2=a^2+b^2[/tex].

Solve for side [tex]b[/tex].

[tex]c^2=a^2+b^2[/tex]

[tex]b=\sqrt{c^2-a^2}[/tex]

[tex]b=\sqrt{13.7^2-9^2}\approx\boxed{9.7}[/tex]

So there you go. If you have any questions feel free to ask.

r3t40