Answer: magnitude = 114.96 lbs, direction = 88.21°
Step-by-step explanation:
Vector A: 150 lbs at 40°
Vector B: 100 lbs at 170°
Slide Vector B onto Vector A so you have a head to tail connection.
Calculate the angle between the vectors (50°).
Use Law of Cosines to find the magnitude of the resultant vector.
Use Law of Sines to find the direction of the resultant vector.
Law of Cosines: c² = a² + b² - 2ab cos θ
Given: a = 150, b = 100, C = 50°
c² = (100)² + (150)² - 2(100)(150) cos 50°
c = 114.96
Law of Sines:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c}\\\\\text{Given: a=150, c=114.96, C=50}^o\\\\\\\dfrac{\sin A}{150}=\dfrac{\sin 50^o}{114.96}\\\\\\\sin A=\dfrac{150\sin 50^o}{114.96}\\\\\\A=\sin^{-1}\bigg(\dfrac{150\sin 50^o}{114.96}\bigg)\\\\\\A=88.21^o[/tex]
