Thread: triangle

Find the value of x, y, and z reduced to the simplest radical form. Please explain! Thank you in advance!

Ooops...forgot diagram...Here it is!

Originally Posted by IHATECHONGAS

Ooops...forgot diagram...Here it is!

ok, because i ws wondering what x, y, and z are you talking about?

so by Pythagoras' theorem:
x = sqrt(y^2 - 4^2) and also x = sqrt(z^2 - 2^2)

=> sqrt(y^2 - 4^2) = sqrt(z^2 - 2^2)
=> y^2 - 16 = z^2 - 4
=> y^2 - z^2 = 12 ..................(1)


by Pythagoras' theorem:
y = sqrt(6^2 - z^2) and also y = sqrt(x^2 + 4^2)
=> sqrt(6^2 - z^2) = sqrt(x^2 + 4^2)
=> 36 - z^2 = x^2 + 16
=> x^2 + z^2 = 20 ...................(2)


by Pythagoras' theorem:
z = sqrt(6^2 - y^2) and also z = sqrt(x^2 + 2^2)
=> sqrt(6^2 - y^2) = sqrt(x^2 + 2^2)
=> 36 - y^2 = x^2 + 4
=> x^2 + y^2 = 32 ....................(3)

So we have the system:
y^2 - z^2 = 12 ..................(1)
x^2 + z^2 = 20 ..................(2)
x^2 + y^2 = 32 ..................(3)

solving this system should give you your values

can you take it from here?