Given:
100 lbs at 50°
50 lbs at 160°
1st vector:
100 lbs cos(50°) = 64.3 lbs ⇒ positive x direction
100 lbs sin(50°) = 76.60 lbs ⇒ positive y direction
2nd vector:
50 lbs cos(160°) = - 46.98 lbs ⇒ negative x direction
50 lbs sin(160°) = 17.10 lbs ⇒ positive y direction
x values:
64.3 lbs + (-46.98 lbs) = 17.32 positive x direction
y values:
76.60 lbs + 17.10 lbs = 93.70 positive y direction
Use Pythagorean theorem to find the resultant.
Positive y direction = long leg of the right triangle
Positive x direction = short leg of the right triangle
Resultant = hypotenuse of the right triangle
a² + b² = c²
93.70² + 17.32² = c²
8779.69 + 299.98 = c²
9079.67 = c²
√9079.67 = √c²
95.29 lbs = c
Resultant is 95.29 lbs.
Direction of the resultang.
Θ = tan^-1 (93.7/17.32) = 79.53° above positive x axis.
