Answer:
R=10,244 Lb
Step-by-step explanation:
In order to solve this problem, we can start by drawing the situation. (See attached picture).
We can look at the forces applied by the trucks as vectors, so in this case, in order to find the resultant force, we can add the two vectors. You can do so by drawing one force after the other and join the start of the first force with the end of the second force to form a triangle. The missing side will be the resultant force. In that triangle I drew there, the inner angle will be found by subtracting 180°-110°=70°
In this case we can find the resultant force by using the law of cosines:
[tex]A^{2}=B^{2}+C^{2}-2AB cos \alpha[/tex]
so we can use the data given by the problem:
[tex]R^{2}=T_{1}^{2}+T_{2}^{2}-2T_{1}T_{2} cos \alpha[/tex]
so we can solve this for R, so we get:
[tex]R=\sqrt{T_{1}^{2}+T_{2}^{2}-2T_{1}T_{2} cos \alpha}[/tex]
now we can substitute:
[tex]R=\sqrt{(10,000Lb)^{2}+(7,500Lb)^{2}-2(10,000Lb)(7,500Lb) cos (70^{0})}[/tex]
which yields:
R=10,244Lb
