Question

Solve for x y and z?

Answer 1

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.