Exploring Pythagorean Triples and Special Right Triangles

This video tutorial explores the Pythagorean theorem, focusing on Pythagorean triples and special right triangles. It begins with an introduction to the theorem and its application in right triangles, followed by a discussion on Pythagorean triples and their integer solutions. The tutorial then delves into special right triangles, specifically the 45-45-90 and 30-60-90 triangles, explaining their properties and how to calculate side lengths using trigonometric functions and the Pythagorean theorem.

What is the result of squaring the sides of a 3-4-5 triangle?

• 6 + 8 = 14

• 9 + 16 = 30

• 9 + 16 = 25

• 6 + 8 = 15

Which of the following is a commonly used Pythagorean triple?

• 8-9-10

• 7-11-14

• 6-10-15

• 5-12-13

What is the scale factor applied to a 3-4-5 triangle to get a 6-8-10 triangle?

• 2

• 3

• 5

• 4

In a 45-45-90 triangle, what is the relationship between the legs and the hypotenuse?

• Legs are equal, hypotenuse is the square root of 2 times a leg

• Legs are equal, hypotenuse is twice a leg

• Legs are in a 2:1 ratio, hypotenuse is equal to one leg

• Legs are in a 1:2 ratio, hypotenuse is the square root of 3 times a leg

What is the tangent of 45 degrees in a 45-45-90 triangle?

• 0.5

• 1.5

• 1

• 2

What is the relationship between the sides of a 45-45-90 triangle?

• 1:1:√2

• 1:1:2

• 1:√2:2

• 1:2:√3

What is the ratio of the hypotenuse to a leg in a 30-60-90 triangle?

• 1:1

• 2:1

• 3:2

• 1:2

What is the sine of 30 degrees in a 30-60-90 triangle?

• 0.707

• 1

• 0.5

• 1.5

How do you calculate the length of the longer leg in a 30-60-90 triangle if the shorter leg is 1?

• Square root of 3

• Square root of 2

• 2

• 3

In a 30-60-90 triangle, if the hypotenuse is 2, what is the length of the shorter leg?

• 2

• √3

• √2

• 1