Will
The sides of a triangle ABC are 6, 7, 8 the smallest angle being C then the length of altitude
from C is
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1
Answer:
ANSWER
5
14
6
If x be the length of internal bisector of ∠ C, then it divides the opposite side in the ratio of arms of the angle.
∴
8
AD
=
7
BD
=
8+7
AD+BD
=
15
6
=
5
2
∴AD=
5
16
Applying cosine formula on ΔADC,
AD
2
=x
2
+8
2
−2.x.8cos
2
C
(
5
16
)
2
=x
2
+64−16x.cos
2
C
...(1)
where cos
2
C
=
ab
s(s−c)
=
4
3
2
3
Hence from (1) on putting for cos
2
C
, we get x=
5
14
6
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