Question

# If the hypotenuse of a 45°-45°-90° triangle has a length of √2, how long are the legs?

Right triangles and trigonometry

If the hypotenuse of a $$45^{\circ}-45^{\circ}-90^{\circ}$$ triangle has a length of $$\displaystyle\sqrt{2}$$, how long are the legs?

A $$45^{\circ}-45^{\circ}-90^{\circ}$$ triangle is a right isosceles triangle. If x is the length of each leg, we can use the Pythagorean Theorem to write: $$\displaystyle{x}^{{2}}+{x}^{{2}}={\left(\sqrt{2}\right)}^{{2}}$$
$$\displaystyle{2}{x}^{{2}}={2}$$
$$\displaystyle{x}^{{2}}={1}$$
$$x=1$$