Properties of 30-60-90 and 45-45-90 Triangles

This video tutorial covers solving special right triangles, focusing on 45-45-90 and 30-60-90 triangles. It reviews the properties and ratios derived from the Pythagorean theorem, providing examples and practice problems. The tutorial emphasizes the importance of exact answers and rationalizing denominators, offering strategies for solving both types of triangles. Reference triangles are introduced as a tool for understanding and solving problems, with a focus on practicing these concepts.

What is the hypotenuse of a 45-45-90 triangle if one leg is 8?

• 8√2

• 8√3

• 16

• 8

If the hypotenuse of a 45-45-90 triangle is 19√2, what is the length of each leg?

• 19/2

• 19

• 19√2/2

• 19√2

In a 30-60-90 triangle, which side is opposite the 30-degree angle?

• The long leg

• The short leg

• None of the above

• The hypotenuse

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

• 1:1:2

• 1:2:√3

• 1:√3:2

• 1:1:√2

If the short leg of a 30-60-90 triangle is 5, what is the length of the hypotenuse?

• 5√3

• 10

• 5

• 5√2

Given a 30-60-90 triangle with a long leg of 9√3, what is the length of the short leg?

• 3√3

• 9√3

• 3

• 9

What is the length of the long leg in a 30-60-90 triangle if the hypotenuse is 18?

• 18√3

• 9

• 9√3

• 18

In a 45-45-90 triangle, if the hypotenuse is 32√2, what is the length of each leg?

• 32√2

• 32

• 16√2

• 16

What is the length of the hypotenuse in a 45-45-90 triangle if one leg is 14?

• 28

• 14√2

• 14√3

• 14

If the hypotenuse of a 30-60-90 triangle is 32, what is the length of the short leg?

• 16

• 16√3

• 32√3

• 32