Question

two forces act on a body so the resultant is a force of 68.3 pounds. the angles between the resultant and the forces measure 46 degrees and 38 degrees. the applied forces have different magnitudes. what is the larger magnitude of these forces? 49.4 pounds 52.7 pounds 41.5 pounds 53.6 pounds

Explanation:

Step1: Use the Law of Sines

Let the two forces be \(F_1\) and \(F_2\). The angle between the two original forces is \(46^{\circ}+ 38^{\circ}=84^{\circ}\).
By the Law of Sines, \(\frac{F_1}{\sin46^{\circ}}=\frac{F_2}{\sin38^{\circ}}=\frac{68.3}{\sin84^{\circ}}\)

Step2: Calculate \(F_1\) and \(F_2\)

First, calculate \(\sin84^{\circ}\approx0.9945\), \(\sin46^{\circ}\approx0.7193\), \(\sin38^{\circ}\approx0.6157\)
\(F_1=\frac{68.3\times\sin46^{\circ}}{\sin84^{\circ}}\approx\frac{68.3\times0.7193}{0.9945}\approx49.4\)
\(F_2=\frac{68.3\times\sin38^{\circ}}{\sin84^{\circ}}\approx\frac{68.3\times0.6157}{0.9945}\approx42.0\)

Answer:

A. 49.4 pounds