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 the resultant force. round to two decimal places in all intermediate steps and in your final answer.

79.53° above positive x axis.

step-by-step explanation:

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.

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: