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

The video tutorial covers special right triangles, focusing on the 45-45-90 and 30-60-90 triangles. It explains the properties and side ratios of these triangles, providing formulas to calculate the sides. The tutorial includes examples to demonstrate how to solve for missing sides in both types of triangles, emphasizing the importance of understanding the ratios and relationships between the sides.

What are the two types of special right triangles discussed?

• 45-45-45 and 30-30-120

• 30-30-120 and 60-60-60

• 30-45-105 and 60-30-90

• 45-45-90 and 30-60-90

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

• 1:1:√2

• 1:√2:2

• 1:√3:2

• √2:√2:2

How do you find the hypotenuse in a 45-45-90 triangle given one leg?

• Leg × √2

• Leg ÷ √2

• Leg × 2

• Leg ÷ 2

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

• 1:√3:2

• √3:1:2

• 1:2:√3

• 1:√2:2

How do you find the longer leg in a 30-60-90 triangle?

• Hypotenuse ÷ √3

• Hypotenuse × √3

• Shorter leg ÷ √3

• Shorter leg × √3

Given the leg of a 45-45-90 triangle is 8, what is the hypotenuse?

• 4√2

• 8√3

• 16

• 8√2

If the hypotenuse of a 45-45-90 triangle is 24, what is the length of one leg?

• 12

• 24√2

• 24

• 12√2

Given the shorter leg of a 30-60-90 triangle is 16, what is the hypotenuse?

• 16√2

• 32√2

• 16√3

• 32

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

• 3

• 6√3

• 3√3

• 6

What is the length of the longer leg in a 30-60-90 triangle if the shorter leg is 3?

• 6

• 9

• 3√2

• 3√3