Exploring Special Right Triangles: 30-60-90 and 45-45-90

What are the acute angles that make a right triangle special?

• Both 30°, 60°, 90° and 45°, 45°, 90°

• 45°, 45°, and 90°

• 30°, 60°, and 90°

• 22.5°, 67.5°, and 90°

In a 45-45-90 triangle, if one leg is 6 units, what is the length of the hypotenuse?

• 12 units

• 6√2 units

• 6 units

• 3√2 units

What is the ratio of sides in a 45-45-90 triangle?

• 1:√3:2

• 1:√2:2

• 1:1:√2

• √2:√2:2

In a 30-60-90 triangle, if the hypotenuse is 6 units, what is the length of the shorter leg?

• 6 units

• 3√3 units

• 6√3 units

• 3 units

What is the ratio of sides in a 30-60-90 triangle?

• 1:1:√2

• 1:√3:2

• √3:√3:2

• 1:2:√3

How do you find the long leg in a 30-60-90 triangle if you know the short leg is 4 units?

• 4√3 units

• 8 units

• 4 units

• 2 units

If the hypotenuse in a 45-45-90 triangle is 14 units, what is the length of each leg?

• 14√2 units

• 7√2 units

• 14 units

• 7 units

What is the process called when you eliminate a radical from the denominator?

• Radicalization

• Rationalization

• Simplification

• Normalization

In a 30-60-90 triangle, if the longer leg is 6 units, what is the length of the hypotenuse?

• 3 units

• 6 units

• 12 units

• 9 units

Why are special right triangles considered 'special'?

• Both A and B are correct.

• They do not follow the Pythagorean theorem.

• Their sides are in a constant ratio.

• They have unique angles.