Question

The sides of a triangle are 5 cm, 12 cm, and 13 cm long. Find the lengths, to the nearest tenth, of the segments into which the bisector of each angle divides the opposite side. Show work and explain your answer and how you got the answer you got. Medal will be rewarded! :D

Answer 1

The bisector of an angle of a triangle divides the opposite side in the ratio of the side containing the bisected angle.

27.
The 13 cm. side is divided in the ratio 5:12, making the two lengths:
5 * 13 / (5 + 12) = 3.8 cm.
12 * 13 / (5 + 12) = 9.2 cm.

The 12 cm. side is divided in the ratio 5:13, giving:
5 * 12 / (5 + 13) = 3.3 cm.
13 * 12 / (5 + 13) = 8.7 cm.

The 5 cm. side is divided in the ratio 12:13, giving:
12 * 5 / (12 + 13) = 2.4 cm.
13 * 5 / (12 + 13) = 2.6 cm.

(All answers to nearest tenth).
this was shown by rackbrane in this website http://answers.yahoo.com/question/index?qid=20100111182621AAhcWWe