Right Triangles

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 can be expressed as: c² = a² + b².

Front

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse, use the Pythagorean theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

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 side opposite the 30-degree angle is the shortest, the side opposite the 60-degree angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of one leg.

Front

How do you calculate the diagonal of a rectangle?

Back

To calculate the diagonal of a rectangle, use the Pythagorean theorem: d = √(length² + width²), where d is the diagonal.

Front

If one leg of a right triangle is 4 cm and the other leg is 3 cm, what is the length of the hypotenuse?

Back

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

Front

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

Back

The area of a right triangle is given by the formula: Area = (1/2) × base × height.

Front

How do you find the length of a missing side in a right triangle?

Back

To find a missing side, use the Pythagorean theorem or the properties of special triangles (30-60-90 or 45-45-90) depending on the information given.

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.