12/4 pythag. application #2

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

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

Back

To determine if a triangle is a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides. If a² + b² = c² holds true, then the triangle is a right triangle.

Front

What are the side lengths of a right triangle?

Back

In a right triangle, the side opposite the right angle is called the hypotenuse, and it is the longest side. The other two sides are called the legs.

Front

If a triangle has sides of lengths 19 feet, 80 feet, and 82 feet, is it a right triangle?

Back

No, because 19² + 80² = 361 + 6400 = 6761, which is not equal to 82² (6724).

Front

What is the formula to calculate the length of the diagonal of a rectangle?

Back

The length of the diagonal (d) of a rectangle can be calculated using the formula: d = √(width² + length²).

Front

If a rectangle is 11 inches tall and 8 inches wide, what is the length of the diagonal?

Back

Using the formula: d = √(11² + 8²) = √(121 + 64) = √185 ≈ 13.6 inches.

Front

What is the distance formula in a right triangle?

Back

The distance formula in a right triangle is derived from the Pythagorean Theorem and is used to find the length of the hypotenuse.

Front

How do you find the diagonal distance across a rectangular field?

Back

To find the diagonal distance across a rectangular field, use the Pythagorean Theorem: d = √(width² + length²).

Front

What is the relationship between the sides of a right triangle and the ladder problem?

Back

In the ladder problem, the distance from the wall and the height the ladder reaches on the wall form a right triangle with the ladder as the hypotenuse.

Front

If a ladder is placed 15 feet from a wall and reaches 8 feet up, how long is the ladder?

Back

Using the Pythagorean Theorem: c = √(15² + 8²) = √(225 + 64) = √289 = 17 feet.