Exploring Special Right Triangles: 45-45-90 and 30-60-90

The video tutorial covers special right triangles, focusing on 45-45-90 and 30-60-90 triangles. It begins with a review of triangle classification by angles, including acute, obtuse, and right triangles, and the use of the Pythagorean theorem. The tutorial then delves into the properties of 45-45-90 triangles, explaining how to calculate the hypotenuse and legs. It also covers 30-60-90 triangles, detailing the relationships between the short leg, long leg, and hypotenuse, with examples to illustrate these concepts.

Which theorem is used in right triangles to find the relationship between their sides?

• Fermat's Last Theorem

• Euclid's theorem

• Pythagorean theorem

• Thales' theorem

In a 45-45-90 triangle, if one leg is 5 units, what is the length of the hypotenuse?

• 7.5 units

• 10 units

• 5√2 units

• 5 units

In a 45-45-90 triangle, how is the hypotenuse related to the leg?

• Hypotenuse is twice the leg

• Hypotenuse is half the leg

• Hypotenuse is equal to the leg

• Hypotenuse is the leg multiplied by √2

How do you find the length of a leg in a 45-45-90 triangle if the hypotenuse is known?

• Divide the hypotenuse by √2

• Divide the hypotenuse by 2

• Multiply the hypotenuse by 2

• Multiply the hypotenuse by √2

If the short leg in a 30-60-90 triangle is 6 units, what is the length of the hypotenuse?

• 12 units

• 6 units

• 18 units

• 6√3 units

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

• Multiply the short leg by √3

• Divide the short leg by 2

• Divide the short leg by √3

• Multiply the short leg by 2

What is the length of the longer leg in a 30-60-90 triangle if the short leg is 3√2 units?

• 6√2 units

• 6 units

• 3√6 units

• 9 units

What is the ratio of the sides in a 30-60-90 triangle?

• 1:√3:2

• 1:√2:2

• 1:1:√2

• 1:2:√3

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

• Multiply by √3

• Divide by 2

• Divide by √3

• Multiply by 2

If the hypotenuse in a 30-60-90 triangle is 50 units, what is the length of the short leg?

• 50 units

• 25√3 units

• 50√3 units

• 25 units