Right Triangle Problems

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 determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length is equal to the sum of the squares of the other two lengths. If c is the longest side, verify if c² = a² + b².

Front

What is the length of the hypotenuse in a right triangle with legs 11.1 and 12.4?

Back

Using the Pythagorean Theorem: c = √(11.1² + 12.4²) = √(123.21 + 153.76) = √(277.97) ≈ 16.7.

Front

What is the length of the hypotenuse in a right triangle with legs 7 and 3?

Back

Using the Pythagorean Theorem: c = √(7² + 3²) = √(49 + 9) = √(58) ≈ 7.6.

Front

What is the formula for finding the length of the diagonal of a rectangular prism?

Back

The length of the diagonal (d) of a rectangular prism can be found using the formula: d = √(l² + w² + h²), where l is the length, w is the width, and h is the height.

Front

If a right triangle has legs of lengths 5 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √(169) = 13.

Front

What is the relationship between the sides of a right triangle?

Back

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

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 crucial for applying the Pythagorean Theorem to find missing side lengths.

Front

Can the lengths 7.5, 8.5, and 4 form a right triangle?

Back

No, because 8.5² is not equal to 7.5² + 4².

Front

What is the length of the incline plane if it reaches a height of 5 feet and the base is 13 feet away?

Back

Using the Pythagorean Theorem: c = √(5² + 13²) = √(25 + 169) = √(194) ≈ 15.