Right Triangle Missing Sides

Front

What is a right triangle?

Back

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

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.

Front

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

Back

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

Front

What is the hypotenuse in a right triangle?

Back

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

Front

How do you determine if three lengths can form a right triangle?

Back

Use the Pythagorean Theorem: If a² + b² = c² holds true for the lengths, they can form a right triangle.

Front

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

Back

The diagonal (d) can be found using the formula d = √(length² + width²).

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

10 (Using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100; √100 = 10).

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

Front

What is the length of the missing side if one leg is 12 and the hypotenuse is 13?

Back

5 (Using the Pythagorean Theorem: 12² + b² = 13²; 144 + b² = 169; b² = 25; b = 5).

Front

What is the area of a right triangle with legs of lengths 5 and 12?

Back

30 (Area = 1/2 * base * height = 1/2 * 5 * 12).