EC - Pythagorean Application

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 diagonal of a rectangle?

Back

To find the length of the diagonal (d) of a rectangle, use the Pythagorean Theorem: d = √(width² + height²).

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.

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, the longer leg is opposite the 60° angle, and the hypotenuse is the longest side.

Front

How do you calculate the distance between two points in a coordinate plane?

Back

The distance (d) between two points (x1, y1) and (x2, y2) can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is a right triangle?

Back

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

Front

If a ladder is leaning against a wall, how can you find the height it reaches?

Back

Use the Pythagorean Theorem: height = √(ladder length² - distance from wall²).

Front

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

Back

The area (A) of a right triangle can be calculated using the formula: A = (1/2) × base × height.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle with sides a, b, and c is a right triangle, check if a² + b² = c², where c is the longest side.

Front

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

Back

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