Exploring Special Right Triangles in Advanced Geometry

What type of triangle is formed by angles of 45, 45, and 90 degrees?

• Scalene triangle

• Isosceles triangle

• Equilateral triangle

• Acute triangle

How is the hypotenuse of a 45-45-90 triangle related to its legs?

• Equal to one leg

• Twice the length of one leg

• √2 times the length of one leg

• Half the length of one leg

In a 45-45-90 triangle, if one leg is 10 units long, what is the length of the hypotenuse?

• 20 units

• 10 units

• 5√2 units

• 10√2 units

What is the ratio of sides in a 45-45-90 triangle?

• 1:1:√2

• 1:√2:2

• 1:1:1

• 1:2:√3

In a 30-60-90 triangle, what is the length of the longer leg if the shorter leg is 4 units?

• 8 units

• 2√3 units

• 4√3 units

• 4 units

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

• 1:√2:√3

• 1:2:√3

• 1:√3:2

• 1:1:√2

If the hypotenuse of a 30-60-90 triangle is 12 units, what is the length of the shorter leg?

• 12√3 units

• 6 units

• 12 units

• 6√3 units

How is the longer leg of a 30-60-90 triangle related to the shorter leg?

• Equal to the shorter leg

• Half the length of the shorter leg

• Twice the length of the shorter leg

• √3 times the length of the shorter leg

What is the length of the hypotenuse in a 30-60-90 triangle if the shorter leg is 4 units?

• 4√3 units

• 8 units

• 4 units

• 2√3 units

If the longer leg of a 30-60-90 triangle is 6√3 units, what is the length of the hypotenuse?

• 6√3 units

• 12√3 units

• 6 units

• 12 units