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 a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

If a right triangle has one leg measuring 3 meters and the other leg measuring 4 meters, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25, so c = 5 meters.

Front

In the equation a² + b² = c², what do 'a' and 'b' represent?

Back

'a' and 'b' represent the lengths of the two legs of a right triangle.

Front

What is the distance between two points (0,0) and (3,4) in a coordinate plane?

Back

Using the distance formula derived from the Pythagorean Theorem: distance = √((3-0)² + (4-0)²) = √(9 + 16) = √25 = 5.

Front

How do you find the length of one leg of a right triangle if you know the lengths of the hypotenuse and the other leg?

Back

You can rearrange the Pythagorean Theorem: a² = c² - b², where 'c' is the hypotenuse and 'b' is the known leg.

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.

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

Back

Using the Pythagorean Theorem: b² = c² - a² = 10² - 8² = 100 - 64 = 36, so b = 6 cm.

Front

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

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.