Pythagorean Theorem: Missing Sides

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 can be expressed as: c² = a² + b².

Front

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

Back

5 cm (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the length of the missing side if the hypotenuse is 10 cm and one side is 6 cm?

Back

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

Front

How do you find the length of a side in a right triangle?

Back

To find the length of a side, use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

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

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

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

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 24 feet, how long is the ladder?

Back

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

Front

What is the formula to calculate the area of a right triangle?

Back

Area = 1/2 * base * height.

Front

If the lengths of the two legs of a right triangle are 8 cm and 15 cm, what is the length of the hypotenuse?

Back

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

Front

What is the definition of a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.