Question

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

Answer 1

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

$\alpha=180-(\gamma+\beta)$
$\alpha=180-(90+49)=\boxed{41}$

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

Now we solve this for hypotenuse.

$\cos(\beta)=\frac{a}{c}$

$c=\frac{a}{\cos(\beta)}$

Now put in the numbers.

$c=\frac{9}{\cos(49)}\approx\boxed{13.7}$

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

Solve for side $b$.

$c^2=a^2+b^2$

$b=\sqrt{c^2-a^2}$

$b=\sqrt{13.7^2-9^2}\approx\boxed{9.7}$

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

r3t40