Pythagorean Theorem - find the hypotenuse

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). This can be expressed as: a² + b² = c².

Front

In a right triangle, which side is the hypotenuse?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 feet.

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

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

Front

How do 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 lengths of the sides satisfy the Pythagorean Theorem: a² + b² = c². If this equation holds true, the triangle is a right triangle.

Front

What are the values of a and b in the equation 5² + 12² = c²?

Back

In the equation 5² + 12² = c², a = 5 and b = 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-degree angle is the shortest, the side opposite the 60-degree angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

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

How can you find the length of one side of a right triangle if you know the hypotenuse and one other side?

Back

You can find the length of the missing side using the Pythagorean Theorem: a² = c² - b² or b² = c² - a², where c is the hypotenuse and a or b is the known side.

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 ensure structures are built correctly.