Chapter 8.1, Problem 95PE

A $50\text{-lb}$ weight is supported from two cables and the system is in equilibrium. The magnitudes of the forces on the cables are denoted by $\left|F_1\left|\text{ and }\right|F_2\right|,$ respectively. An engineering student knows that the horizontal components of the two forces (shown in red) must be equal in magnitude. Furthermore, the sum of the magnitudes of the vertical components of the forces (shown in blue) must be equal to $50\text{-lb}$ to offset the downward force of the weight. Find the values of $\left|F_1\left|\text{ and }\right|F_2\right|.$ Write the answers in exact form with no radical in the denominator. Also give approximations to 1 decimal place.