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For the life of me I cannot understand part B. What does F(BA) and the 60 degree angle have to do with the projection of 500# on AC? Why can we just assume that the angle at C is 180-(45+60)?

Thanks

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2 Answers 2

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The question is poorly worded. They intended to ask for "the component in the direction of AC of the 500 lb force," which is found as the solution shows.

To find $\beta$, the writer uses the property of any triangle that all its angles add to 180°.

Nonetheless, the solution writer's approach is not the one I would have used. Like you, I think the line AB is not relevant to the question. Using the geometrical parameters given, I would have expressed the force $\vec F_{500}$ as a vector with a magnitude and direction, then expressed the direction of AC as a unit vector $\hat n$, then taken the dot product $\vec F_{500} \cdot \hat n$.

In fact, I'm doubting whether the solution given is even correct.

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You can answer your own question if you remember how to draw the vector/force diagram as shown below.

enter image description here

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