Understanding Special Right Triangles

The video tutorial begins with an introduction to 45-45-90 triangles, explaining that the non-hypotenuse sides are equal to the square root of 2 over 2 times the hypotenuse. The instructor demonstrates this with examples and verifies the formula using the Pythagorean theorem. The tutorial then introduces 30-60-90 triangles, explaining their properties by constructing an equilateral triangle and using the Pythagorean theorem to derive the side lengths relative to the hypotenuse. The video concludes with a brief mention of how these concepts can be useful for solving problems quickly, especially in standardized tests.

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

• Each side is half the hypotenuse.

• Each side is twice the hypotenuse.

• Each side is equal to the hypotenuse.

• Each side is the square root of 2 over 2 times the hypotenuse.

In a 45-45-90 triangle with a hypotenuse of 10, what is the length of each leg?

• 5

• 5√2

• 10√2

• 5√3

How can you verify the side lengths of a 45-45-90 triangle?

• Using the Law of Cosines

• Using the area formula

• Using the Pythagorean theorem

• Using the Law of Sines

What are the angles in a 30-60-90 triangle?

• 60, 60, 60

• 30, 45, 105

• 45, 45, 90

• 30, 60, 90

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

• Equal to the hypotenuse

• Half the hypotenuse

• Twice the hypotenuse

• The same as the side opposite the 60-degree angle

What is the relationship between the sides of a 30-60-90 triangle?

• All sides are equal.

• The side opposite the 30-degree angle is half the hypotenuse.

• The side opposite the 60-degree angle is half the hypotenuse.

• The side opposite the 90-degree angle is half the hypotenuse.

How do you derive the side opposite the 60-degree angle in a 30-60-90 triangle?

• It is twice the hypotenuse.

• It is the square root of 3 over 2 times the hypotenuse.

• It is equal to the hypotenuse.

• It is half the hypotenuse.

What is the significance of doubling a 30-60-90 triangle?

• It forms a right triangle.

• It forms an equilateral triangle.

• It forms a square.

• It forms a rectangle.

Why is it useful to memorize the properties of 30-60-90 triangles?

• They are rarely used in tests.

• They are not applicable in real life.

• They help solve problems quickly.

• They are only used in advanced mathematics.

What is the length of the side opposite the 60-degree angle in a 30-60-90 triangle?

• The square root of 3 over 2 times the hypotenuse

• Half the hypotenuse

• Equal to the hypotenuse

• Twice the hypotenuse