Understanding Special Right Triangles and Their Applications

What is the relationship between the legs and hypotenuse in a 45-45-90 triangle?

• The hypotenuse is the leg times the square root of 3.

• The hypotenuse is equal to the leg.

• The hypotenuse is twice the length of a leg.

• The hypotenuse is the leg times the square root of 2.

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

• x times the square root of 3

• x times the square root of 2

• 2x

• x

If the hypotenuse of a 45-45-90 triangle is 16 cm, what is the length of each leg?

• 16 cm

• 16 square root of 2 cm

• 8 square root of 2 cm

• 8 cm

What is the altitude of an equilateral triangle with a perimeter of 36 inches?

• 12 square root of 3 inches

• 12 inches

• 6 square root of 3 inches

• 6 inches

How do you find the hypotenuse of a 45-45-90 triangle formed by folding a square bandana with side 40 cm?

• Multiply the side by 2

• Divide the side by the square root of 2

• Multiply the side by the square root of 2

• Divide the side by 2

A support post forms a 30-degree angle with the top of an 18-foot wall. What is the length of the post?

• 18 feet

• 20.8 feet

• 6 square root of 3 feet

• 12 square root of 3 feet

In a 45-45-90 triangle, if the hypotenuse is 6, what is the length of each leg?

• 3 square root of 2

• 6

• 3

• 6 square root of 2

In a 30-60-90 triangle, if the hypotenuse is 3 square root of 2, what is the length of the short leg?

• 3 square root of 2 over 2

• 3

• 3 over 2

• 3 square root of 2

What is the perimeter of a hexagon formed by a rectangle and special right triangles, given sides 8 and 6?

• 8 square root of 3 plus 6 square root of 2 plus 26

• 8 square root of 3 plus 4 square root of 2 plus 26

• 6 square root of 3 plus 8 square root of 2 plus 26

• 6 square root of 3 plus 4 square root of 2 plus 26

In a 30-60-90 triangle, if the short leg is 6, what is the length of the long leg?

• 12

• 6 square root of 3

• 6

• 12 square root of 3