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

How do you find the length of the missing side in a right triangle using the Pythagorean theorem?

Back

To find the length of the missing side, rearrange the Pythagorean theorem formula. If you know the lengths of two sides, you can calculate the third side. For example, if you know a and c, you can find b using b = √(c² - a²).

Front

What is a right triangle?

Back

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

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the side opposite the right angle is called the hypotenuse, and it is the longest side. The other two sides are referred to as the legs.

Front

If a triangle has sides of lengths 8, 14, and 16, how can you determine if it is acute, right, or obtuse?

Back

To determine the type of triangle, compare the square of the longest side (16²) with the sum of the squares of the other two sides (8² + 14²). If the longest side squared is greater, the triangle is obtuse; if it is equal, it is right; if it is less, it is acute.

Front

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

Back

The formula to calculate the hypotenuse (c) of a right triangle is c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

In the context of the Pythagorean theorem, what does 'c' represent?

Back

In the context of the Pythagorean theorem, 'c' represents the length of the hypotenuse of a right triangle.

Front

What is the distance from the top of a ladder to the base of a wall if the ladder is 10 feet long and the bottom is 4 feet from the wall?

Back

Using the Pythagorean theorem, the distance from the top of the ladder to the base of the wall is approximately 9 feet.

Front

What is the significance of the Pythagorean theorem in real-life applications?

Back

The Pythagorean theorem is used in various real-life applications, including construction, navigation, and physics, to calculate distances and angles.

Front

How can you verify if a triangle with sides 2.1, 7.2, and 7.5 is a right triangle?

Back

To verify if the triangle is a right triangle, check if a² + b² = c² holds true, where c is the longest side. In this case, 2.1² + 7.2² should equal 7.5².