Special Right Triangles Mixed

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 adical{2} $$, where$$ x@@ is the length of each leg.

A special right triangle with angles measuring 30°, 60°, and 90°. The sides are in the ratio 1 : @@ adical{3}@@ : 2, where 1 is the length of the side opposite the 30° angle.

The hypotenuse is @@8 adical{2}@@.

The longer leg is @@4 adical{3}@@.

The hypotenuse is twice the length of the shorter leg.

The lengths of the legs are equal, and the hypotenuse is @@ adical{2}@@ times the length of a leg.

The shorter leg is 6.

@@x = 5 adical{2}@@.

Area = $$\frac{1}{2} \times \text{(shorter leg)} \times \text{(longer leg)}$$ .

The angles measure 45°, 45°, and 90°.