Question

I need to know what X y and z is

Answer 1

You have 3 right-angled triangles so you apply the Pythagoras theorem

z^2 = 4^2 + y^2......(1)

x^2 = 6^2 + y^2 .....(2)            Also taking the large triangle:-

x^2 + z^2 = 10^2.......(3)

Subtracting equation  (1) from equation 2:-

x^2 - z^2 = 20 .......(4)

Adding (3) + (4):-

2x^2 = 120 
x^2 = 60 
x = sqrt 60

So , using equation (4)  z^2 =  x^2 - 20 = 60 - 20 = 40

z = sqrt 40  

now we can find y by substituting in equation (1)

y^2 = z^2 - 4^2 = 40 - 16 =  24

y = sqrt 24