Right Triangle Properties and Pythagorean Theorem

This video tutorial covers solving special right triangles, specifically 45-45-90 and 30-60-90 triangles. It explains the patterns and formulas needed to find missing sides, including the use of radicals. The video also discusses Pythagorean triples and their application in solving right triangles. Example problems are provided to illustrate these concepts.

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

• Leg, Leg, Hypotenuse times radical 2

• Leg, Leg, Hypotenuse times radical 3

• Leg, Leg, Leg times radical 2

• Leg, Leg, Leg times radical 3

If one leg of a 45-45-90 triangle is 7, what is the hypotenuse?

• 14 radical 2

• 14

• 7 radical 2

• 7

How do you find the legs of a 45-45-90 triangle if the hypotenuse is given as 8?

• Multiply the hypotenuse by radical 2

• Divide the hypotenuse by radical 2

• Divide the hypotenuse by 2

• Multiply the hypotenuse by 2

What is the pattern for the sides of a 30-60-90 triangle?

• Short leg, Long leg times 2, Hypotenuse times radical 3

• Short leg, Hypotenuse times 2, Long leg times radical 3

• Short leg, Hypotenuse, Long leg times radical 3

• Short leg, Long leg, Hypotenuse

If the short leg of a 30-60-90 triangle is 8, what is the hypotenuse?

• 16

• 16 radical 3

• 8 radical 3

• 8

How do you find the short leg of a 30-60-90 triangle if the hypotenuse is 12?

• Divide the hypotenuse by 2

• Multiply the hypotenuse by 2

• Divide the hypotenuse by radical 3

• Multiply the hypotenuse by radical 3

What is a Pythagorean triple?

• A set of three numbers that form a scalene triangle

• A set of three numbers that form an isosceles triangle

• A set of three numbers that form an equilateral triangle

• A set of three numbers that satisfy the Pythagorean theorem

Which of the following is a common Pythagorean triple?

• 6, 8, 10

• 5, 6, 7

• 3, 4, 5

• 2, 3, 4

If a right triangle has sides 6 and 8, what is the length of the hypotenuse?

• 10

• 12

• 16

• 14

If a right triangle has sides 24 and 26, what is the length of the third side?

• 10

• 12

• 16

• 14