Pythagorean Theorem (Finding the Legs)

Front

What is the Pythagorean Theorem?

Back

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 is expressed as: a² + b² = c².

Front

What does 'a' and 'b' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the legs (the two shorter sides) of a right triangle.

Front

What does 'c' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'c' represents the length of the hypotenuse, which is the longest side of a right triangle, opposite the right angle.

Front

If a = 3 and b = 4, what is c?

Back

Using the Pythagorean Theorem: c² = a² + b² = 3² + 4² = 9 + 16 = 25. Therefore, c = 5.

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles, which have one angle measuring 90 degrees.

Front

What is the formula to find the length of a leg if the hypotenuse and the other leg are known?

Back

If c is the hypotenuse and b is the known leg, the formula to find the unknown leg (a) is: a = √(c² - b²).

Front

If the hypotenuse is 10 and one leg is 6, what is the length of the other leg?

Back

Using the formula: a = √(c² - b²) = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What type of angle is formed by the legs of a right triangle?

Back

The legs of a right triangle form a right angle, which measures 90 degrees.

Front

In a right triangle, if one leg is 8 and the hypotenuse is 10, what is the length of the other leg?

Back

Using the formula: b = √(c² - a²) = √(10² - 8²) = √(100 - 64) = √36 = 6.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides satisfy the Pythagorean Theorem: 3² + 4² = 5² (9 + 16 = 25).