Respuesta :
Answer:
The bisector of angle A divides side a into segments of 6 cm and 14 cm.
The bisector of angle B divides side b into segments of 6 cm and 8 cm.
Step-by-step explanation:
Let's denote the sides of the triangle as follows:
- Side a = 6 cm (opposite angle A)
- Side b = 14 cm (opposite angle B)
- Side c = 15 cm (opposite angle C)
1. First, find the length of the bisector segment dividing side a:
- Use the Angle Bisector Theorem to find the length of the segment by setting up a proportion:
(Length of segment on side b)/(Length of segment on side c) = (Length of side b)/(Length of side c)
Let x be the length of the segment on side a.
x/15 = 14/15
x = 14
The bisector of angle A divides side a into segments of 6 cm and 14 cm.
2. Next, find the lengths of the segments into which the bisector of angle B divides side b:
- Using the same process as above, we set up the proportion:
(Length of segment on side a)/(Length of segment on side c) = (Length of side a)/(Length of side c)
Let y be the length of the segment on side b.
y/15 = 6/15
y = 6
The bisector of angle B divides side b into segments of 6 cm and 8 cm.
