Understanding 30-60-90 Triangles

This video tutorial explains the properties and rules of 30-60-90 triangles, focusing on how to determine the lengths of the sides based on given information. It covers three scenarios: when the short leg, long leg, or hypotenuse is provided. The tutorial also includes practice problems to reinforce the concepts and methods discussed.

What is the general rule for the hypotenuse in a 30-60-90 triangle?

• It is the same as the long leg.

• It is twice the short leg.

• It is half the long leg.

• It is equal to the short leg.

If the short leg of a 30-60-90 triangle is 7, what is the length of the long leg?

• 14√3

• 7

• 7√3

• 14

When given the long leg of a 30-60-90 triangle, what is the first step to find the short leg?

• Multiply by 2

• Divide by √3

• Multiply by √3

• Add 3

If the long leg of a 30-60-90 triangle is 4√3, what is the short leg?

• 2

• 4

• 4√3

• 8

What is the short leg if the hypotenuse of a 30-60-90 triangle is 46?

• 46

• 23√3

• 46√3

• 23

In a 30-60-90 triangle, if the hypotenuse is 46, what is the long leg?

• 23

• 23√3

• 46

• 46√3

What is the length of the hypotenuse if the short leg is 12 in a 30-60-90 triangle?

• 12

• 12√3

• 24

• 24√3

If the long leg is 15 in a 30-60-90 triangle, what is the short leg after rationalizing the denominator?

• 15√3

• 5

• 5√3

• 15

What is the hypotenuse if the short leg is 5√3 in a 30-60-90 triangle?

• 5

• 10

• 10√3

• 5√3

In a 30-60-90 triangle, if the long leg is 15, what is the hypotenuse?

• 15

• 15√3

• 30

• 10√3