SOLUTION: Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 40° and 170°, respectively. Find the direction and magnitude of the resultant force. Round to two dec

Algebra ->  Vectors -> SOLUTION: Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 40° and 170°, respectively. Find the direction and magnitude of the resultant force. Round to two dec      Log On


   

Question 1091486: Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 40° and 170°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Please show work so i can understand!!
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
sin(40) = vertical component / 150
vertical component = sin(40) * 150 = 96.4181 = 96.42
cos(40) = horizontal component / 150
horizontal component = cos(40) * 150 = 114.9066 = 114.91
:
sin(170) = vertical component / 100
vertical component = sin(170) * 100 = 17.3648 = 17.36
cos(170) = horizontal component / 100
horizontal component = cos(170) * 100 = −98.4807 = −98.48
:
summing the horizontal components = 114.91 -98.48 = 16.43
summing the vertical components = 96.42 + 17.36 = 113.78
:
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the magnitude of the resultant vector = square root(16.43^2 + 113.78^2) = 114.96
the direction of the resultant vector = tan^(-1) (113.78 / 16.43) = 81.78 degrees
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