30-60-90 Triangle Problems

The video tutorial covers the properties of 30-60-90 triangles, emphasizing the relationships between the angles and sides. It provides two example problems: one with a hypotenuse of 12 and another with a side of 5, demonstrating how to calculate the other sides using known formulas. The tutorial also explains the process of rationalizing denominators and concludes with encouragement to tackle more advanced Pythagorean theorem problems.

What is the length of the side opposite the 30-degree angle in a 30-60-90 triangle if the hypotenuse is 10?

• 10

• 10√3

• 5

• 5√3

In a 30-60-90 triangle, if the side opposite the 30-degree angle is 4, what is the length of the hypotenuse?

• 4

• 8

• 8√3

• 4√3

What is the length of the side opposite the 30-degree angle if the hypotenuse is 20?

• 10

• 20

• 10√3

• 20√3

In a 30-60-90 triangle, if the hypotenuse is 12, what is the length of the side opposite the 60-degree angle?

• 12√3

• 6√3

• 6

• 12

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

• The longer side is half the shorter side.

• The longer side is √3 times the shorter side.

• The longer side is twice the shorter side.

• The longer side is equal to the shorter side.

If the hypotenuse of a 30-60-90 triangle is 14, what is the length of the side opposite the 60-degree angle?

• 7

• 7√3

• 14

• 14√3

If the side opposite the 60-degree angle in a 30-60-90 triangle is 5, what is the length of the hypotenuse?

• 5√3

• 10/√3

• 10√3

• 5

What is the first step in solving for the hypotenuse if the side opposite the 60-degree angle is given?

• Divide by 2

• Multiply by 2

• Divide by √3/2

• Multiply by √3/2

Why is it generally preferred to rationalize the denominator in mathematical expressions?

• It simplifies the expression.

• It avoids irrational numbers in the denominator.

• It is a standard mathematical practice.

• It makes calculations easier.

What is the length of the side opposite the 30-degree angle if the hypotenuse is 10√3/3?

• 5/3

• 10/3

• 5√3/3

• 10√3