Question

1. solve the triangle below.

Explanation:

Step1: Find angle A

The sum of angles in a triangle is 180°. Since angle C = 90° and angle B = 55°, then $A=180^{\circ}-90^{\circ}-55^{\circ}=35^{\circ}$.

Step2: Find side BC

We know $\tan B=\frac{AC}{BC}$. Given $AC = 9$ and $B = 55^{\circ}$, then $BC=\frac{AC}{\tan B}=\frac{9}{\tan55^{\circ}}\approx\frac{9}{1.4281}\approx6.3$.

Step3: Find side AB

We know $\sin B=\frac{AC}{AB}$. Given $AC = 9$ and $B = 55^{\circ}$, then $AB=\frac{AC}{\sin B}=\frac{9}{\sin55^{\circ}}\approx\frac{9}{0.8192}\approx10.99$.

Answer:

Angle $A = 35^{\circ}$, side $BC\approx6.3$, side $AB\approx10.99$