Question

Use the figure to find x

Answer 1

The value of x is
`(7√(6))/(2)`

Solution given:

AB=7

BD=x

<BAC=60°

<DBC=45°

In right angled triangle ABC

Tan 60°=opposite/adjacent

Tan 60°=BC/AB

Substitute value

`√(3)`=
`(BC)/(7)`

BC=
`7√(3)`

again

In right angled triangle BCD

Using Cos angle

Cos 45=adjacent/hypotenuse

Cos45°=BD/BC

Substituting value

`(√(2))/(2)=(x)/(7√(3))`

Doing criss cross multiplication

`(√(2))/(2)*7√(3)=x`

x=
`(7√(6))/(2)`