Pythagorean theorem and its applications.

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.

Tags

CCSS.8.G.B.8

Front

What is the formula to find the length of side 'a' in a right triangle if 'b' and 'c' are known?

Back

The formula to find the length of side 'a' is: a = √(c² - b²).

Tags

CCSS.8.G.B.7

Front

If a right triangle has legs of lengths 3 cm and 4 cm, what is the length of the hypotenuse?

Back

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

Tags

CCSS.8.G.B.7

Front

What is the area of a square with a side length of 6 cm?

Back

The area of a square is calculated as side². Therefore, area = 6² = 36 cm².

Tags

CCSS.4.MD.A.3

CCSS.3.MD.C.7B

Front

In a right triangle, if one leg is 12 cm and the hypotenuse is 15 cm, what is the length of the other leg?

Back

Using the Pythagorean theorem: b = √(c² - a²) = √(15² - 12²) = √(225 - 144) = √81 = 9 cm.

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 shortest side is opposite the 30° angle.

Tags

CCSS.HSG.CO.C.10

Front

How do you calculate the distance from a point to a line using the Pythagorean theorem?

Back

To calculate the distance from a point to a line, drop a perpendicular from the point to the line, forming a right triangle. Use the Pythagorean theorem to find the length of the perpendicular.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for applying the Pythagorean theorem.

Tags

CCSS.8.G.B.8

Front

If the area of a square is 64 cm², what is the length of one side?

Back

The length of one side is found by taking the square root of the area: side = √64 = 8 cm.

Tags

CCSS.4.MD.A.3

CCSS.3.MD.C.7B

Front

What is the formula for the area of a right triangle?

Back

The area of a right triangle is calculated as: Area = (1/2) × base × height.

Tags

CCSS.6.G.A.1