Pythagorean Theorem

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). It can be expressed as: a² + b² = c².

The Pythagorean Theorem ONLY works for right triangles.

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 cm.

Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8 cm.

To find the length of a side in a right triangle, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

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

Using the Pythagorean Theorem: 10² + 24² = c²; 100 + 576 = c²; 676 = c²; c = 26 feet.

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

Using the Pythagorean Theorem: 8² + 15² = c²; 64 + 225 = c²; 289 = c²; c = 17 cm.