Question

the hypotenuse of a right angle triangle is 17 cm long if one of the remaining two sides is 8 cm in length feild the length of other side

Answer 1

We are given the hypotenuse and the length of one side.
Let the unknown side be x.
By Pythagorean theorem,
a²+b²=c²
So,
8²+x² = 17²
x²=225
x² = 15²
x=15 
Thus the length of the other side is 15cm.

Answer 2

Let the length of the unkown side be $x$ cm. 
We know that, in Pythagoras Theorem, sum of squares of two sides is equal to square of hypotenuse. It's something like this : $x^{2} + 8^{2} = 17^{2}$ This rule is only applicable for right triangles. 
Here 17 cm is the length of hypotenuse, 8 cm is the length of one leg of the right triangle and x cm is the length of the unknown side of the triangle, which is also a leg of right triangle. Solve for x in the equation. 
$x^{2} + 8^{2} = 17^{2}$
$x^{2} = 17^{2} - 8^{2} = 289 - 64 = 225$
$x^{2} = 225$
$\sqrt{x^{2}} = \sqrt{225}$
$x = 15$
∴ The length of the other side is 15 cm. 

Hope you understood well.