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: a² + b² = c².

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

If one side of a right triangle is 14 and the hypotenuse is 20, how can you find the length of the other side?

Back

You can use the Pythagorean Theorem: x² + 14² = 20². Solve for x.

Front

What is the value of 15²?

Back

15² = 225.

Front

How do you solve for x in the equation 15² + x² = 21²?

Back

First, calculate 15² and 21². Then, rearrange the equation to isolate x²: x² = 21² - 15². Finally, take the square root of both sides to find x.

Front

What is the formula to calculate 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

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, where 1 is the length of the side opposite the 30-degree angle, √3 is the length of the side opposite the 60-degree angle, and 2 is the length of the hypotenuse.

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 length of the hypotenuse is √2 times the length of each leg.

Front

How can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side: a² + b² = c².

Front

What is the significance of the Pythagorean Theorem in real-world applications?

Back

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