Understanding 30-60-90 Triangles

What makes 30-60-90 triangles special in geometry?

• They have all sides equal.

• They form an equilateral triangle when mirrored.

• They have all angles equal.

• They are the only triangles with a right angle.

In a 30-60-90 triangle, what is the ratio of the side opposite the 30-degree angle to the hypotenuse?

• 1:√3

• 1:2

• 2:1

• 1:1

How is the height of a 30-60-90 triangle derived using the Pythagorean theorem?

• By setting the height equal to the hypotenuse.

• By using the formula a^2 + b^2 = c^2.

• By adding the squares of all sides.

• By subtracting the square of the shorter side from the square of the hypotenuse.

If the side opposite the 30-degree angle is 4, what is the length of the hypotenuse?

• 4√3

• 8

• 2

• 4

Given the hypotenuse of a 30-60-90 triangle is 20, what is the length of the side opposite the 30-degree angle?

• 10√3

• 20

• 10

• 5

If the side opposite the 60-degree angle is 9, what is the length of the side opposite the 30-degree angle?

• 3√3

• 9√3

• 9

• 3

What is the length of the hypotenuse if the side opposite the 60-degree angle is 10√3?

• 10

• 10√3

• 20√3

• 20

How do you rationalize the expression 9/√3?

• Multiply by √3/√3

• Subtract 3

• Divide by 3

• Add 3

What is the simplified form of 9√3/3?

• 3√3

• 9

• 3

• √3

Where can you find more practice questions on 30-60-90 triangles?

• geometryhelp.net

• mathpractice.com

• mathsucks.org

• mathsducks.org