The ends of a rope are fastened at separate but horizontal points on a ceiling. A 
weight is hung from the rope such that the two segments of the rope make angles of 
and 
with the ceiling. Compute the tension in each segment of the rope.
Extracted from R. L. Gray. (1973). Physics Problems: Mechanics and Heat.
Solution.
Draw a free-body diagram below:
Separating the vertical and the horizontal component:
we have two equations with two unknowns (i.e., 
and 
).
The rest is left the reader as an exercise.