Question

Solve AABC. Round your answers to the nearest hundredth, if necessary

Answer 1

Answer:

$C=25^{\circ},\\a\approx 10.72,\\b\approx 11.83$

Step-by-step explanation:

The sum of the interior angles of a triangle is 180 degrees. Thus, angle C must be $180-90-65=25^{\circ}$.

In any triangle, the Law of Sines is given by $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$.

Therefore, we have:

$\frac{\sin 90^{\circ}}{b}=\frac{\sin 25^{\circ}}{5},\\\\b=\frac{5\sin90^{\circ}}{\sin 25^{\circ}}=11.8310079158\approx \boxed{11.83}$

$\frac{a}{\sin 65^{\circ}}=\frac{5}{\sin25^{\circ}},\\a=\frac{5\sin 65^{\circ}}{\sin25^{\circ}}=10.7225346025\approx \boxed{10.72}$