ABC is a right angled isosceles triangle with `/_B=90^@` If D is a point on AB such that `/_CDB=15^@` and if `AD=35cm` then CD is equal to

Options

A. `35sqrt2` cm
B. `70sqrt2cm`
C. `(35 sqrt3)/2 cm`
D. `35sqrt6` cm

Answer

A

Explanation

In `DeltaBCD , tan 15^(@) = (BC)/(BD)`
`(1-1/sqrt3)/(1+1/sqrt3) = x/(x+35)`

` Rightarrow (sqrt3 -1)/(sqrt3+1) = x/(x + 35)`
` Rightarrow sqrt3x + 35sqrt3 -x - 35 =sqrt3x+x`
` x= (35 (sqrt3-1))/2`
`CD= sqrt((35/2)^(2){(sqrt3+1)+(sqrt3-1)^(2)})`
` = 35/2 xx 2sqrt2 = 35sqrt2` cm