Step-by-Step Solution
Step 1
We are given the value of force $F = 3{\rm{50 lb}}$.
We are asked to estimate the magnitudes of the two components of F.
Step 2
The relation to convert the force from pound into newton is,
Since $1\;{\rm{lb}} = {\rm{4}}{\rm{.448}}\;{\rm{N}}$, then\begin{array}{c} 3{\rm{50 lb}} = \left( {350\;{\rm{lb}} \times \frac{{{\rm{4}}{\rm{.448}}\;{\rm{N}}}}{{1\;{\rm{lb}}}}} \right)\\ = 1556.8\;{\rm{N}} \end{array}
The following is the free body diagram to calculate the magnitude of force.
To find the magnitude of force we will use the law of sines.\[\frac{{{F_{AB}}}}{{\sin 60^\circ }} = \frac{F}{{\sin 75^\circ }}\]
Plugging the known values in the above equation.\begin{array}{c} \frac{{{F_{AB}}}}{{\sin 60^\circ }} = \frac{{1556.8\;{\rm{N}}}}{{\sin 75^\circ }}\\ {F_{AB}} = 1395.8\;{\rm{N}} \end{array}
Step 3
The following is the free body diagram to calculate the magnitude of force.
To find the magnitude of force we will use the law of sines.\[\frac{{{F_{AC}}}}{{\sin 45^\circ }} = \frac{F}{{\sin 75^\circ }}\]
Plugging the known values in the above equation.\begin{array}{c} \frac{{{F_{AC}}}}{{\sin 45^\circ }} = \frac{{1556.8\;{\rm{N}}}}{{\sin 75^\circ }}\\ {F_{AC}} = 1139.6\;{\rm{N}} \end{array}