Two forces with magnitudes of 100 and 50 pounds act on an object at angles of 50° and 160° respectively. Find the direction and magnitude of these forces. Round to two decimal places in all intermediate steps and in your final answer.

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.