Pythagorean Theorem (Missing Leg)

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.

Tags

CCSS.8.G.B.8

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are typically referred to as sides 'a' and 'b' in the Pythagorean Theorem.

Front

How do you find the length of a missing leg in a right triangle?

Back

To find the length of a missing leg in a right triangle, you can rearrange the Pythagorean Theorem formula. If you know the length of the hypotenuse (c) and one leg (a), you can find the other leg (b) using the formula: b = √(c² - a²).

Tags

CCSS.8.G.B.7

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 (1), the side opposite the 60-degree angle is √3, and the hypotenuse is 2.

Tags

CCSS.HSG.CO.C.10

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 'a', then the hypotenuse is a√2.

Tags

CCSS.8.G.B.8

Front

What is the formula to calculate the hypotenuse if both legs are known?

Back

If both legs (a and b) of a right triangle are known, the hypotenuse (c) can be calculated using the formula: c = √(a² + b²).

Tags

CCSS.8.G.B.8

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 determine distances and relationships between different points.

Tags

CCSS.8.G.B.8

Front

How can the Pythagorean Theorem be applied to find distances in coordinate geometry?

Back

In coordinate geometry, the distance between two points (x₁, y₁) and (x₂, y₂) can be found using the Pythagorean Theorem: Distance = √((x₂ - x₁)² + (y₂ - y₁)²).

Tags

CCSS.6.G.A.3

Front

What is the value of the hypotenuse in a right triangle with legs of length 3 and 4?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Tags

CCSS.8.G.B.7

Front

If one leg of a right triangle is 5 and the hypotenuse is 13, what is the length of the other leg?

Back

Using the formula: b = √(c² - a²), where c = 13 and a = 5: b = √(13² - 5²) = √(169 - 25) = √144 = 12.

Tags

CCSS.8.G.B.7