Question

Can someone explain how to do this? :)

Answer 1

Therefore x = 4 units , $y = 2\sqrt{3}$ units and z =8

Step-by-step explanation:

We know that,

$cos\theta = \frac{\textre{base}}{hypoteneous}$

$\Leftrightarrow$$cos45^\circ = \frac{x}{4\sqrt{2} }$

$\Leftrightarrow \frac{1}{\sqrt{2}} =\frac{x}{4\sqrt{2} }$

$\Leftrightarrow x=\frac{4\sqrt{2} }{\sqrt{2}}$

$\Leftrightarrow x =4$

The median of the triangle is =$\sqrt{(4\sqrt{2})^2-4^2 }$       = 4

Again

$Sin 60 ^\circ = \frac{y}{z}$

$\Leftrightarrow \frac{\sqrt{3} }{2}=\frac{y}{z}$

$\Leftrightarrow z\frac{\sqrt{3} }{2}={y}$.........(1)

and  

$y^2 + 4^2 =z^2$

putting $y= z\frac{\sqrt{3} }{2}$ we get

$(z\frac{\sqrt{3} }{2}) ^2 + 4^2 =z^2$

$\Leftrightarrow \frac{3}{4} z^2+16 =z^2$

$\Leftrightarrow \frac {1}{4} z^2= 16$

$\Leftrightarrow z^2= 16 \times 4$

$\Leftrightarrow z= 8$

Therefore

$y = 4\times \frac{\sqrt{3} }{2}$

$\Leftrightarrow y = 2\sqrt{3}$

Therefore x = 4 units , $y = 2\sqrt{3}$ units and z =8