SOLUTION: Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of these forces. Round to two decimal place

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Question 981278: Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of these forces. Round to two decimal places in all intermediate steps and in your final answer.
Please help! I would like to understand the steps to get to the answer!
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of these forces.
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One is 25 pounds at 10 degs
The other is 30 pounds at 100 degs
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I don't know where the angles are measured from, it's not stated.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I assume that the answer wanted is the direction and magnitude of the resultant of those forces.
I also assume that the angles are measured counter-clockwise from the positive x-axis, as shown below.
The angle between the forces is 100%5Eo-10%5Eo=90%5Eo .
Based on that angle we can find the magnitude of the resultant force,
and the angles between the resultant force and the two given forces.
Leaving out the x- and y-axes, the two forces and their resultant force can be drawn as a rectangle with its diagonal, like this
The magnitude (in lb) of the resultant, red%28R%29 , is
the lengths of the hypotenuse of a right triangle with legs measuring 25 and 30 :
sqrt%2830%5E3%2B25%5E2%29=sqrt%28900%2B325%29=sqrt%281525%29=61sqrt%285%29= about 39.05 (rounded).
The angle red%28R%29 makes with the 25 pound force is red%28theta%29 such that
tan%28red%28theta%29%29=30%2F25=1.2 ---> red%28theta%29=about+50.19%5Eo (rounded)
So the angle between the positive x-axis and the resultant measures about
10%5Eo%2B50.19%5Eo=highlight%2860.19%5Eo%29 (rounded),
and the magnitude of the resultant is about highlight%2839.05%29 pounds (rounded).