Understanding 30-60-90 Right Triangles

This video tutorial covers the properties and solving techniques for 30-60-90 right triangles. It explains why these triangles are special, focusing on their consistent patterns. The tutorial guides viewers through identifying the short and long legs based on angles and applying the pattern to calculate side lengths. An example problem is solved, demonstrating the use of these patterns to find the lengths of the triangle's sides.

What makes a 30-60-90 triangle special?

• It is always scalene.

• It has a consistent pattern for side lengths.

• It is always isosceles.

• It has equal sides.

Which angle is opposite the short leg in a 30-60-90 triangle?

• 60 degrees

• 90 degrees

• 45 degrees

• 30 degrees

How do you find the long leg in a 30-60-90 triangle?

• Multiply the hypotenuse by the square root of 3

• Multiply the short leg by 2

• Multiply the hypotenuse by 2

• Multiply the short leg by the square root of 3

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

• 2 times the long leg

• 2 times the short leg

• Square root of 3 times the long leg

• Square root of 3 times the short leg

If the short leg of a 30-60-90 triangle is 5, what is the hypotenuse?

• 10

• 15

• 5√3

• 5

In a 30-60-90 triangle, if the short leg is 7, what is the long leg?

• 14

• 7

• 21

• 7√3

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 three times the short leg.

• The hypotenuse is the same as the short leg.

• The hypotenuse is twice the short leg.

If the long leg of a 30-60-90 triangle is 9√3, what is the short leg?

• 9

• 6

• 12

• 3

Which side is opposite the 60-degree angle in a 30-60-90 triangle?

• Short leg

• Long leg

• Hypotenuse

• None of the above

What is the length of the hypotenuse if the short leg is 8?

• 16

• 24

• 8√3

• 8