Answer:
[tex]x = 24\sqrt{3}[/tex]
y=24
z=48
Step-by-step explanation:
To find x, y, and z, use special triangles 45-45-90 and 30-60-90. A 45-45-90 triangle has standard side lengths [tex]1-1-\sqrt{2}[/tex]. Since the 45-45-90 in the picture has a side length of [tex]24\sqrt{6}[/tex] then its [tex]24\sqrt{3} * \sqrt{2}[/tex]. This triangle has been multiplied by a factor of [tex]24\sqrt{3}[/tex].
We multiply the side length x which corresponds to 1 in the 45-45-90 triangle by [tex]24\sqrt{3}[/tex]. This means [tex]x=24\sqrt{3}[/tex].
The other triangle is a 30-60-90 special triangle which has side lengths [tex]1-\sqrt{3} -2[/tex]. x corresponds to the [tex]\sqrt{3}[/tex] side length. This means y corresponds to the side length 1. This means y is 24 from [tex]24\sqrt{3}[/tex]. And z is the final side length which corresponds to side length 2. So it is 48 or 2*24=48.
