Exploring Special Right Triangles (30-60-90)

The video tutorial explores the properties of equilateral triangles and their angles, focusing on the 30-60-90 triangle. It explains how folding an equilateral triangle along its symmetry line affects its angles and introduces the Pythagorean theorem to find side lengths. The tutorial generalizes the pattern for side lengths in 30-60-90 triangles and provides examples, including non-standard cases, to illustrate these concepts.

What is the angle measure of each corner in an equilateral triangle?

• 60 degrees

• 90 degrees

• 45 degrees

• 30 degrees

What happens to the top angle when an equilateral triangle is folded along a line of symmetry?

• It remains 60 degrees

• It becomes 90 degrees

• It is halved to 30 degrees

• It doubles to 120 degrees

Using the Pythagorean theorem, what is the length of the second leg if one leg is 1 and the hypotenuse is 2?

• 1

• Square root of 3

• 2

• Square root of 2

What pattern emerges for the third side's length in a 30-60-90 triangle?

• Leg length times square root of 2

• Leg length squared

• Leg length times 2

• Leg length times square root of 3

If the short leg of a 30-60-90 triangle is 3, what is the length of the hypotenuse?

• 12

• 3

• 6

• 9

For a 30-60-90 triangle, how is the hypotenuse related to the short leg?

• It is twice the length

• It is the same length

• It is three times the length

• It is half the length

What is the length of the longer leg if the short leg is 4 in a 30-60-90 triangle?

• 8 square root of 3

• 8

• 4

• 4 square root of 3

How do you adjust the calculation for a 30-60-90 triangle when the short leg does not fit the standard pattern?

• Halve the hypotenuse

• Double the short leg

• Multiply the short leg by square root of 3

• Square the short leg

If the hypotenuse is given as 4 root 3, what is the short leg's length?

• 4 root 3

• 4

• 2 root 3

• 2

What is the correct approach to find the hypotenuse if the short leg is known in a non-standard 30-60-90 triangle?

• Multiply the short leg by root 3

• Square the short leg

• Divide the short leg by 2

• Multiply the short leg by 2