30-60-90 Triangle Problems

This video tutorial covers special right triangles, focusing on 30-60-90 and 45-45-90 triangles. It explains the properties and ratios of these triangles and provides step-by-step solutions to various problems. The video also explores equilateral triangles, calculating altitudes, and solving related word problems.

What are the two types of special right triangles discussed in the video?

• 30-30-60 and 45-45-90

• 30-60-90 and 45-45-90

• 30-60-90 and 60-60-60

• 45-45-90 and 60-60-60

In a 30-60-90 triangle, what is the ratio of the sides opposite the 30-degree, 60-degree, and 90-degree angles?

• 2 : 1 : √3

• 1 : √3 : 2

• 1 : 2 : √3

• √3 : 1 : 2

If the short side of a 30-60-90 triangle is 8, what is the length of the hypotenuse?

• 8√3

• 16

• 8

• 4√3

In a 30-60-90 triangle, if the medium side is 12, what is the length of the short side?

• 4√3

• 12√3

• 4

• 12/√3

What is the relationship between the hypotenuse and the short side in a 30-60-90 triangle?

• The hypotenuse is √3 times the short side

• The hypotenuse is equal to the short side

• The hypotenuse is twice the short side

• The hypotenuse is half the short side

In an equilateral triangle, what is the measure of each angle?

• 60 degrees

• 90 degrees

• 45 degrees

• 30 degrees

How does the altitude of an equilateral triangle relate to its sides?

• It bisects the base and forms two 30-60-90 triangles

• It is equal to the side length

• It is half the side length

• It forms a 45-45-90 triangle

If the altitude of an equilateral triangle is 18, what is the length of the side?

• 36

• 12√3

• 24

• 18√3

What is the length of the altitude in a 30-60-90 triangle if the short side is 5?

• 15

• 5

• 10

• 5√3

In a 30-60-90 triangle, if the hypotenuse is 16, what is the length of the short side?

• 4

• 16

• 8

• 8√3