In Triangle QRS, m

Question

In Triangle QRS, m<Q = 70, mR = 44, and m<S = 66. Which side of Triangle QRS is the shortest?
 A.Cannot be determined
 B.QS
 C.QR
 D.RS

anonymous · Answer

m<R=44 ******

mww · Answer

Set up the sine rule for each side in relation to each angle.
You should get QS/sin44 = QR/sin66 = RS/sin70
Then rewrite these equations in terms of either QS, QR or QS
For instance QS = (sin44/sin66) QR and RS = (sin70/sin66) QR
Now we can tell which one is larger based on the values of the fractions.
sin44/sin66 < 1 and sin70/sin66 > 1. so RS > QR > QS.
Therefore QS is the shortest length. The key is to convert the sine rule into two equations involving a single variable and compare between them ratiowise.