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: c² = a² + b².

The hypotenuse is the longest side of a right triangle, opposite the right angle.

10 (Using the Pythagorean Theorem: 6² + 8² = c², 36 + 64 = c², 100 = c², c = 10).

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

4 (Using the Pythagorean Theorem: 5² = 3² + b², 25 = 9 + b², b² = 16, b = 4).

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 each leg.

12 (Using the Pythagorean Theorem: 13² = 5² + b², 169 = 25 + b², b² = 144, b = 12).

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.