Answer:
x = 6, y =√45 and z = √180.
If you want the answer correct to nearest hundredth
x = 6.00, y = 6.71 and z = 13.42.
Explanation:
y^2 = x^2 + 9 (By the Pythagoras theorem)
z^2 = x^2 + 144 (.....................................................)
So , by subtraction:
z^2 - y^2 = 135......A
Using Similar triangles:
y/15 = 3/y
y^2 = 45
y = √45
So substituting in equation A:
z^2 - 45 = 135
z^2 = 180
z = √180.
180 = x^2 + 144 (By Pythagoras theorem)
x^2 = 180 - 144
x^2 = 36
x = 6.