Right Triangle Review (sub)

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: a² + b² = c².

Front

What are the side lengths 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 a leg.

Front

What are the side lengths of a 30°-60°-90° triangle?

Back

In a 30°-60°-90° triangle, the length of the side opposite the 30° angle is half the length of the hypotenuse, and the length of the side opposite the 60° angle is √3 times the length of the shorter leg.

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

If one leg of a right triangle is 9 inches and the other leg is 12 inches, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c = √(9² + 12²) = √(81 + 144) = √225 = 15 inches.

Front

What is the relationship between the angles in a right triangle?

Back

In a right triangle, the sum of the three angles is always 180 degrees, with one angle being 90 degrees.

Front

What is the definition of the hypotenuse?

Back

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

Front

How do you calculate the area of a right triangle?

Back

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

Front

If the base of a right triangle is 10 inches and the height is 5 inches, what is the area?

Back

Area = (1/2) × 10 × 5 = 25 square inches.