Finding Missing Side Lengths in Special Right Triangles

The video tutorial covers special right triangles, focusing on 45-45-90 and 30-60-90 triangles. It explains the consistent patterns in these triangles due to their similarity. For 45-45-90 triangles, both legs are equal, and the hypotenuse is the leg times the square root of 2. For 30-60-90 triangles, the short leg is opposite the 30-degree angle, the long leg is the short leg times the square root of 3, and the hypotenuse is twice the short leg. The tutorial includes examples of solving these triangles, both forward and backward, and rationalizing results.

What is the pattern for the sides of a 45-45-90 triangle?

• x, x, x√3

• x, x√2, x√2

• x, x, x√2

• x, x√3, 2x

How do you find the hypotenuse in a 45-45-90 triangle if one leg is x?

• 2x

• x√3

• x√2

• x + x

In a 30-60-90 triangle, how is the long leg related to the short leg?

• It is half the short leg.

• It is the short leg multiplied by √3.

• It is the short leg multiplied by √2.

• It is double the short leg.

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

• x√2

• x + x

• 2x

• x√3

If the hypotenuse of a 45-45-90 triangle is 8√2, what is the length of one leg?

• 4√2

• 8√2

• 4

• 8

What is the process to find a leg in a 45-45-90 triangle given the hypotenuse?

• Multiply the hypotenuse by √2

• Divide the hypotenuse by 2

• Divide the hypotenuse by √2

• Multiply the hypotenuse by 2

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

• 6√3

• 12√3

• 6

• 4√3

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

• Multiply the short leg by 2

• Multiply the short leg by √2

• Multiply the short leg by √3

• Divide the short leg by √3

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

• The hypotenuse is double the short leg.

• The hypotenuse is the short leg multiplied by √2.

• The hypotenuse is half the short leg.

• The hypotenuse is the short leg multiplied by √3.

If given the long leg of a 30-60-90 triangle, how do you find the short leg?

• Divide by 2

• Multiply by 2

• Divide by √3

• Multiply by √3