Question

I need help on this.

Answer 1

Well, that triangle is an isosceles, it's also a right triangle. The BC side is the hypotenuse and the sides of unknown length are equal.
We have the Pythagorean theorem:
BC ^ 2 = CA ^ 2 + CB ^ 2
As CA = CB
BC ^ 2 = 2 * CA ^ 2
CA = CB = square root (BC ^ 2/2)
Good luck!
M.

Answer 2

For 45, 45, 90 angled triangles, the two legs are equal to 'x', and the hypotenuse is equal to $\sf x\sqrt{2}$. Since we know the length of the hypotenuse, we can set this equal to it:

$\sf x\sqrt{2}=8$

Divide the square root of 2 to both sides:

$\boxed{\sf x\approx 5.657}$

So the length of both AC and BC is approximately 5.657.