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 can be expressed as: c² = a² + b².

Front

If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?

Back

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

Front

What is the length of the missing side if the hypotenuse is 13 and one side is 5?

Back

Using the Pythagorean Theorem: 13² = 5² + b². Thus, 169 = 25 + b², which gives b² = 144. Therefore, b = √144 = 12.

Front

In a right triangle, if the lengths of the two legs are equal, what is the relationship between the legs and the hypotenuse?

Back

If the legs are equal (let's say both are 'a'), then the hypotenuse (c) can be calculated as c = a√2.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a right triangle has a hypotenuse of 15 and one leg of 9, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 15² = 9² + b². Thus, 225 = 81 + b², which gives b² = 144. Therefore, b = √144 = 12.

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 side opposite the 30° angle is 'x', the side opposite the 60° angle is 'x√3', and the hypotenuse is '2x'.

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. If each leg is 'x', then the hypotenuse is 'x√2'.

Front

How do you find the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) × base × height.

Front

If a rectangular field is 40 yards wide and 30 yards long, what is the length of the diagonal?

Back

Using the Pythagorean Theorem: d² = 40² + 30² = 1600 + 900 = 2500. Therefore, d = √2500 = 50 yards.