Pythagorean Theorem

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: c² = a² + b².

Front

What is the hypotenuse in a right triangle?

Back

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

Front

Calculate 19².

Back

361

Front

If one side of a right triangle is 3 and the other side is 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

Find the missing side if one side is 6 and the hypotenuse is 10.

Back

8 (Using the Pythagorean Theorem: 6² + b² = 10², so 36 + b² = 100, thus b² = 64, and b = √64 = 8).

Front

What is the formula to find the length of a side in a right triangle?

Back

The formula is derived from the Pythagorean Theorem: a² + b² = c².

Front

Estimate the hypotenuse of a right triangle with sides 8 and 15 to the nearest tenth.

Back

17.0 (Using the Pythagorean Theorem: √(8² + 15²) = √(64 + 225) = √289 = 17).

Front

If the hypotenuse is 13 and one side is 5, what is the length of the other side?

Back

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

Front

What does 'a' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'a' represents the length of one of the two legs (sides) of a right triangle.

Front

What does 'b' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'b' represents the length of the other leg (side) of a right triangle.