Question

FInd X without calculator.

Answer 1

Heya!!!

Let the total length of BC = 100 + z

IN TRANGLE ABC

Tan ( 60 ) = ( z + 100 ) / x

=>

1/√3 = ( z + 100 ) / x

=>

x = ( z√3 + 100√3 )..... equation ( i )

NOW , IN TRANGLE ABD

Tan ( 45 ) = z / x

=>

z = x

Now, put value of z in above equation

x = x√3 + 100√3

=>

x - x√3 = 100√3

=>

x = 100√3 / ( 1 - √3 )

RATIONALIZE THE DENOMINATOR

x = 100√3 ( 1 + √3 ) / -2

=>

x = (100√3 + 100×9 )/ -2

=>

x = (900 + 100√3 ) /-2

=>

x = -50 ( 9 + √3 )

LENGTH CAN'T BE NEGATIVE SO, WE TAKE ITS MAGNITUDE

x = 50 ( 9 + √3 ) units