Special Right Triangles

A special right triangle where the angles are 45°, 45°, and 90°. The sides opposite the 45° angles are equal, and the hypotenuse is $$x\text{√}2$$ , where $$x$$ is the length of each leg.

A special right triangle where the angles are 30°, 60°, and 90°. The sides are in the ratio 1 : $$√3$$ : 2, where the side opposite the 30° angle is $$x$$ , the side opposite the 60° angle is $$x√3$$ , and the hypotenuse is $$2x$$ .

In a 45°-45°-90° triangle, if each leg is $$x$$ , then the hypotenuse is $$x√2$$ .

In a 30°-60°-90° triangle, if the shorter leg (opposite the 30° angle) is $$x$$ , then the longer leg (opposite the 60° angle) is $$x√3$$ and the hypotenuse is $$2x$$ .

The hypotenuse is $$10√2$$ .

The longer leg is $$5√3$$ .

The shorter leg is $$6$$ .

The hypotenuse is $$20$$ .

The area is $$32$$ (Area = 1/2 * base * height = 1/2 * 8 * 8).

The perimeter is $$4 + 4√3 + 8$$ .