Special Right Triangles

What is the value of the longer leg in a 30-60-90 triangle if the shorter leg is 5?

• 5

• 5√2

• 5√3

• 10

How can you verify if a triangle is a right triangle using the Pythagorean theorem?

• Check if the square of the length of the longest side equals the sum of the squares of the lengths of the other two sides.

• Ensure that all three sides are equal in length.

• Measure the angles and confirm one is 90 degrees.

• Calculate the perimeter and check if it is an even number.

What is the relationship between the sides of a 30-60-90 triangle?

• The side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is √3 times the length of the shorter leg.

• All sides are equal in length.

• The side opposite the 30-degree angle is equal to the hypotenuse, and the side opposite the 60-degree angle is half the length of the hypotenuse.

• The side opposite the 30-degree angle is √2 times the length of the hypotenuse, and the side opposite the 60-degree angle is equal to the hypotenuse.

What is the length of the hypotenuse in a 45-45-90 triangle with legs of length 6?

• 6

• 12

• 6√2

• 8

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

• Area = base * height

• Area = (1/2) * base * height

• Area = base + height

• Area = (1/2) * (base + height)

If one leg of a 30-60-90 triangle is 4, what is the length of the hypotenuse?

• 6

• 8

• 10

• 12

What is the value of the hypotenuse in a 30-60-90 triangle if the shorter leg is 5?

• 8

• 9

• 10

• 12

What is the Pythagorean theorem?

• 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): c² = a² + b².

• The sum of the angles in a triangle is equal to 180 degrees.

• The area of a circle is calculated using the formula A = πr².

• In any triangle, the longest side is always opposite the largest angle.

How do you calculate the length of a leg in a 45-45-90 triangle if the hypotenuse is known?

• Multiply the length of the hypotenuse by √2 to find the length of each leg.

• Divide the length of the hypotenuse by 2 to find the length of each leg.

• Divide the length of the hypotenuse by √2 to find the length of each leg.

• Subtract the length of the hypotenuse from 1 to find the length of each leg.

What are the properties of a 45-45-90 triangle?

• The legs are of equal length, and the hypotenuse is equal to the length of a leg multiplied by √2.

• The legs are of different lengths, and the hypotenuse is the sum of the legs.

• All sides are equal in length, making it an equilateral triangle.

• The hypotenuse is twice the length of one leg.