Question

If ΔABC is a right triangle such that ∠C = 90°, ∠A = 45° and BC =7units, find ∠B, AB and AC.

Answer 1

∠C = 90°, ∠A = 45°
∠A + ∠B + ∠C = 180°
45° + ∠B + 90° = 180°
∠B = 180° - 135°
∠= 45°

sin45° = ${\displaystyle \frac{\text{BC}}{\text{AB}}}$

⇒ AB = ${\displaystyle \frac{\text{BC}}{\text{sin45°}}}$

⇒ AB = ${\displaystyle \frac{7}{\frac{1}{\sqrt{2}}}}$
⇒ AB = ${\displaystyle 7\sqrt{2}\text{units}}$
Also,

tan45° = ${\displaystyle \frac{\text{BC}}{\text{AC}}}$

⇒ AC = ${\displaystyle \frac{\text{BC}}{\tan 45}°}$

⇒ AC = ${\displaystyle \frac{7}{1}}$
⇒ AC = 7units.