Answer: a = 11.24 B = 75.5° C = 53.5°
Step-by-step explanation:
Use Law of Cosines to find a: a² = b² + c² - 2bc · cos A
Given: b = 14, c = 6, A = 51°
a² = (14)² + (6)² - 2(14)(6) · cos 51°
a² = 196 + 36 - 168 · cos 51°
a² = 232 - 105.72
a² = 126.27
a = 11.24
Use Law of Sines to find B: [tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]
Given: A = 51°, a = 11.24, b = 14
[tex]\dfrac{\sin 51^o}{11.24}=\dfrac{\sin B}{14}\\\\\\\dfrac{14\sin51^o}{11.24}=\sin B\\\\\\\sin^{-1}\bigg(\dfrac{14\sin51^o}{11.24}\bigg)=B\\\\\\75.5^0=B[/tex]
Use Triangle Sum Theorem to find C: A + B + C = 180°
Given: A = 51°, B = 75.5°
51° + 75.5° + C = 180°
126.5° + C = 180°
C = 53.5°
