Question

1. solve the triangle below.

Explanation:

Step1: Find angle A

The sum of angles in a triangle is 180°. Given angle B = 55° and angle C = 90° (right - angled triangle as indicated by the right - angle symbol). So, $A=180^{\circ}-(90^{\circ} + 55^{\circ})=35^{\circ}$.

Step2: Find side BC using tangent

We know that $\tan A=\frac{BC}{AC}$. Given $AC = 9$ and $A = 35^{\circ}$. So, $BC=AC\times\tan A=9\times\tan(35^{\circ})\approx9\times0.7002 = 6.3018\approx6.3$.

Step3: Find side AB using cosine

We know that $\cos A=\frac{AC}{AB}$. So, $AB=\frac{AC}{\cos A}=\frac{9}{\cos(35^{\circ})}=\frac{9}{0.8192}\approx10.9985\approx11$.

Answer:

Angle $A = 35^{\circ}$, side $BC\approx6.3$, side $AB\approx11$