Question

Angle ABC of a right angled triangle is bisected by segment beady. The lengths of sides AB and BC are given in the figure. Find the exact length of BD.

Answer 1

The exact length of
`BD` would be
`6.70`

Explanation:

Given
`BC=10\ and\ AB=6`

Also, ∠
`DBC=x` and ∠
`ABD=x`

So, ∠
`ABC=`∠
`DBC+`∠
`ABD=x+x=2x`

Now, in Δ
`ABC`

`cos(2x)=(AB)/(BC)\\\\cos(2x)=(6)/(10)\\\\cos(2x)=0.6\\\\taking\ cos^(-1)\ both\ side\ we\ get, \\\\2x=cos^(-1)(0.6)\\\\2x=53.13\\\\x=(53.13)/(2)=26.56`

Now, in Δ
`ABD`

`cos(26.56)=(AB)/(BD)\\\\cos(26.56)=(6)/(BD)\\\\0.895=(6)/(BD)\\\\BD=(6)/(0.895)\\\\BD=6.70`

So, the exact length of
`BD` would be
`6.70`