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

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) (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) (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 .
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, , is
the lengths of the hypotenuse of a right triangle with legs measuring and :
= about (rounded).
The angle makes with the 25 pound force is such that
---> (rounded)
So the angle between the positive x-axis and the resultant measures about
(rounded),
and the magnitude of the resultant is about pounds (rounded).
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