please help math

Question

Two forces with magnitudes of 90 and 50 pounds act on an object at angles of 30° 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.

Answer 1

two forces of 90 and 50 lbs act on an object at angles 30 and 160 degrees

what is the direction and magnitude of the resultant force

construct a parallelogram with sides 90 and 50

calculate the diagonal using the Law of Cosines

that diagonal = the magnitude of the resultant force

d^2= a^2 + b^2 -2abCosD

d^2 = 90^2 +50^2 -2(90)(5))Cos(160-30)

d = about 128.00 lbs.

then use the Law of Sines to find the direction

SinD/d = SinA/a

solve for SinA, then find A with the Inverse Sine function