Exploring Special Right Triangles

This video tutorial covers the properties and solving techniques for special right triangles, specifically 45-45-90 and 30-60-90 triangles. It explains how to label the sides correctly and solve for unknowns using given side lengths. The tutorial also addresses more complex problems involving mixed triangle types and provides strategies for rationalizing denominators and recognizing patterns in triangle side relationships.

What does having two equal angles in a triangle imply about its sides?

• The sides opposite the equal angles are also equal.

• The sides form an arithmetic sequence.

• The sides are all different lengths.

• The triangle is always obtuse.

In a 45-45-90 triangle, if one leg is 8 units, what is the length of the hypotenuse?

• 16 units

• 8√2 units

• 8 units

• 4√2 units

What is the relationship between the legs of a 45-45-90 triangle?

• They are congruent.

• One is double the other.

• They are perpendicular.

• They form a linear pair.

How do you label the sides of a 30-60-90 triangle?

• X, X, X√2

• X, 2X, X√3

• X, X√3, 2X

• 2X, X, X√3

In a 30-60-90 triangle, if the hypotenuse is 20 units, what is the length of the longer leg?

• 10√3 units

• 10 units

• 20√3 units

• 5√3 units

How is the hypotenuse of a 30-60-90 triangle related to its shortest leg?

• It is triple the length.

• It is double the length.

• It is equal in length.

• It is half the length.

If the longer leg of a 30-60-90 triangle measures 21 units, what is the length of the hypotenuse?

• 21/√3 units

• 42 units

• 14 units

• 21√3 units

In a 30-60-90 triangle, if the longer leg is 14√3, what is the length of the shortest leg?

• 14 units

• 14√3 units

• 7 units

• 28 units

If the hypotenuse of a 45-45-90 triangle is 32√2, what is the length of one leg?

• 32 units

• 16 units

• 64 units

• 32√2 units

When solving a double triangle problem involving a 45-45-90 triangle and a 30-60-90 triangle, what is the first step?

• Label all sides of both triangles.

• Identify the type of each triangle.

• Solve the 45-45-90 triangle first.

• Solve the 30-60-90 triangle first.