In a 30°-60°-90° triangle, the lengths of the sides are in the ratio 1:√3:2. The side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

In a 45°-45°-90° triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

If the shortest side (opposite the 30° angle) is known, the hypotenuse can be found by multiplying the shortest side by 2.

The longer leg (opposite the 60° angle) can be found by multiplying the shortest side by √3.

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

In a right triangle, the sum of the angles is always 180°. If one angle is 90°, the other two angles must sum to 90°.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².