Understanding 30-60-90 Triangles

The video tutorial explains how to solve 30-60-90 triangles using specific rules. It covers three methods: when the short leg, hypotenuse, or long leg is given. The short leg is opposite the 30° angle, the long leg is opposite the 60° angle, and the hypotenuse is opposite the right angle. The tutorial provides step-by-step instructions for each scenario, emphasizing the relationships between the sides and the angles.

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

• The hypotenuse is half the short leg.

• The hypotenuse is twice the short leg.

• The hypotenuse is three times the short leg.

• The hypotenuse is equal to the short leg.

If the short leg of a 30-60-90 triangle is 4, what is the length of the longer leg?

• 6

• 2√3

• 8

• 4√3

How do you find the short leg if the hypotenuse is given in a 30-60-90 triangle?

• Divide the hypotenuse by √3.

• Multiply the hypotenuse by √3.

• Divide the hypotenuse by 2.

• Multiply the hypotenuse by 2.

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the short leg?

• 8

• 12

• 4

• 6

What is the first step in finding the short leg when the longer leg is known in a 30-60-90 triangle?

• Multiply the longer leg by √3.

• Divide the longer leg by √3.

• Divide the longer leg by 2.

• Multiply the longer leg by 2.

If the longer leg of a 30-60-90 triangle is 6√3, what is the length of the short leg?

• 2

• 4

• 3

• 6

How do you rationalize the denominator when dividing by √3?

• Add √3 to both numerator and denominator.

• Multiply both numerator and denominator by 2.

• Multiply both numerator and denominator by √3.

• Divide both numerator and denominator by 3.

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

• 15

• 10

• 5

• 10√3

In a 30-60-90 triangle, what is the ratio of the short leg to the hypotenuse?

• 2:3

• 1:√3

• 1:2

• 1:1

What is the main challenge when finding the short leg from the longer leg in a 30-60-90 triangle?

• Determining the area of the triangle.

• Finding the angle measures.

• Rationalizing the denominator.

• Calculating the hypotenuse.