Answer:
AB = 15
m∠A = 53.1°
m∠B = 36.9°
Step-by-step explanation:
From the picture attached,
By Applying Pythagoras theorem,
AB² = AC² + BC²
AB² = 9² + (12)²
AB² = 81 + 144
AB = √225
AB = 15
tan(B) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{12}{9}[/tex]
= 1.3333
B = [tex]\text{tan}^{-1}(1.3333)[/tex]
= 53.13
≈ 53.1°
Since, m∠A + m∠B + m∠C = 180°
m∠A + 53.1° + 90° = 180°
m∠A = 180°- 143.1°
= 36.9°
