Question

Use the figure to find x

Answer 1

Answer:

The value of x is $\frac{7\sqrt{6}}{2}$

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

$\sqrt{3}$=$\frac{BC}{7}$

BC=$7\sqrt{3}$

again

In right angled triangle BCD

Using Cos angle

Cos 45=adjacent/hypotenuse

Cos45°=BD/BC

Substituting value

$\frac{\sqrt{2}}{2}=\frac{x}{7\sqrt{3}}$

Doing criss cross multiplication

$\frac{\sqrt{2}}{2}*7\sqrt{3}=x$

x=$\frac{7\sqrt{6}}{2}$