Special Right Triangles Review

Special Right Triangles

Review

Deriving the Ratios of the Sides

30-60-90 Triangles

30-60-90 Triangle

• Side length are always in these proportions

• We will use this when we are deriving the Unit Circle

Using the ratios to solve triangles

• Determine what you are given: short leg, long leg, or hypotenuse

• Then use the given side and its ratio to find the variable

• Make sure you rationalize the denominator

Multiple Choice

• a=√6   b=√2
• a=4   b=2
• a=√6   b=2
• a=2   b4

Multiple Choice

What are x and y in this 30-60-90 triangle?

• x = 6 y = 3√3
• x = 1.5√3 y =1.5
• x = 3√3 y = 6
• x = √3 y = 2√3

Multiple Choice

What is the measure of side c?

• 6
• 6√2
• 6√3
• 12

Multiple Choice

Find x.

• 10
• 20
• 10√3
• √3

Multiple Choice

Find x.

• 4
• 2
• √3
• 2√2

Multiple Choice

Find x.

• 10
• √3
• 5
• 10√3

Deriving the Ratios of the Sides

45-45-90 Triangles

45-45-90 Triangle

• Side length are always in these proportions

• Congruent angles have congruent sides across from them

• We will use this when deriving the Unit Circle.

Using the ratios to solve triangles

• Determine what you are given: short leg, long leg, or hypotenuse

• Then use the given side and its ratio to find the variable

• Make sure you rationalize the denominator

Multiple Choice

Determine the value of c.

• c = 6√3

• c = 12√3

• c = 18

• c = 18√2

Multiple Choice

Determine the value of x.

• x = 10√2

• x = 10

• x = 5√3

• x = 5√6

Multiple Choice

Use the 45-45-90 theorem to solve for the hypotenuse.

• 16

• 8

• 8√2

• √16

Multiple Choice

Find x - the length of the hypotenuse of the triangle.

• 5
• 5√2
• 10
• 5√3

Multiple Choice

What is the measure of side c?

• 7

• $\frac{7}{\sqrt{2}}$

• 7√2

• 14

Multiple Choice

Find x.

• 12
• √2
• √3
• 6