Right Triangles Unit Review

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 two shorter sides of a right triangle called?

Back

The two shorter sides of a right triangle are called the 'legs'.

Front

If a right triangle has legs of length 4, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c = √(4² + 4²) = √(16 + 16) = √32 = 4√2.

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the shorter leg is 8?

Back

In a 30-60-90 triangle, the hypotenuse is twice the length of the shorter leg. Therefore, the hypotenuse is 2 * 8 = 16.

Front

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

Back

In a right triangle, one angle is always 90 degrees, and the sum of the other two angles is always 90 degrees.

Front

How do you find the length of a side in a right triangle if you know the lengths of the other two sides?

Back

You can use the Pythagorean theorem: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) and b = √(c² - a²) for the legs.

Front

What is the formula for 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

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

Back

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

Front

What is a 45-45-90 triangle?

Back

A 45-45-90 triangle is an isosceles right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees. The lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

Front

If the hypotenuse of a right triangle is 10 and one leg is 6, what is the length of the other leg?

Back

Using the Pythagorean theorem: b = √(10² - 6²) = √(100 - 36) = √64 = 8.