Answer :
The magnitude of the resultant force when two forces of 167 lb and 181 lb are acting at an angle of 145°42' is approximately 333 lb.
To find the magnitude of the resultant force when two forces are acting at a point, we use the law of cosines. This is a formula used in mathematics to calculate the side of a triangle when the length of two other sides and their enclosed angle are known. The formula is b = √(a² + c² - 2ac*cos(B)), where:
- a and c are the lengths of the two sides of the triangle,
- B is the angle between these sides,
- b is the length of the other side.
The forces given in the problem can be imagined as sides of a triangle with the angle between them given as 145°42' = 145.7° after converting from degrees and minutes to decimal degrees.
Therefore, we can insert our values into the formula. Here, a and c are the forces 167 lb and 181 lb, B is the angle 145.7°.
Let's calculate:
First, we convert the angle from degrees to radians because the cos function in the formula uses radians:
145.7° ≈ 2.54 rad.
Then, we apply the law of cosines:
b = √((167)² + (181)² - 2*167*181*cos(2.54)) ≈ 332.55 lb.
And, as the task requires us to round the result to the nearest pound, we have:
b ≈ 333 lb.
So, the magnitude of the resultant force when two forces of 167 lb and 181 lb are acting at an angle of 145°42' is approximately 333 lb.
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