30-60-90 and 45-45-90 Triangles

The video tutorial explains two special right triangles: the 45-45-90 and the 30-60-90 triangles. It covers the properties and formulas for each type, including how the side lengths relate to the angles. The 45-45-90 triangle is isosceles, with the hypotenuse being the square root of two times longer than the legs. The 30-60-90 triangle has sides in a ratio of 1:√3:2. The video includes examples to demonstrate how to apply these properties and formulas to solve problems involving these triangles.

What are the angles in a 45-45-90 triangle?

• 45, 45, 90 degrees

• 90, 90, 90 degrees

• 30, 60, 90 degrees

• 60, 60, 60 degrees

In a 45-45-90 triangle, what is true about the two legs?

• They are different lengths

• They are equal in length

• One is twice the length of the other

• They are both longer than the hypotenuse

How does the hypotenuse compare to the legs in a 45-45-90 triangle?

• It is half the length of the legs

• It is the square root of two times the length of the legs

• It is twice the length of the legs

• It is the same length as the legs

What is the defining characteristic of a 45-45-90 triangle?

• All sides are equal

• The hypotenuse is three times the length of the legs

• It has a right angle and two 60-degree angles

• Two angles are 45 degrees

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

• 90, 90, 90 degrees

• 60, 60, 60 degrees

• 45, 45, 90 degrees

• 30, 60, 90 degrees

In a 30-60-90 triangle, what is the relationship between the hypotenuse and the shortest side?

• The hypotenuse is half the length of the shortest side

• The hypotenuse is the square root of three times the length of the shortest side

• The hypotenuse is the same length as the shortest side

• The hypotenuse is twice the length of the shortest side

In a 30-60-90 triangle, what is the relationship between the middle side and the shortest side?

• The middle side is twice the length of the shortest side

• The middle side is the same length as the shortest side

• The middle side is the square root of three times the length of the shortest side

• The middle side is half the length of the shortest side

What is the defining characteristic of a 30-60-90 triangle?

• It has a right angle and two 45-degree angles

• All sides are equal

• The middle side is twice the length of the shortest side

• The hypotenuse is twice the length of the shortest side

In a 45-45-90 triangle, if one leg is 3, what is the length of the hypotenuse?

• 3√2

• 6

• 9

• 3

In a 45-45-90 triangle, if the hypotenuse is 5√2, what is the length of each leg?

• 5√2

• 5

• 10

• 2.5