Unit 8 - Right Triangles Test Review

Simplifying Radicals

100

√81

9

200

√80

4√5 is the most simplified answer

this is technically equal to 2√20 but this can be simplified more

300

5√12 x 2√3

60, because 5√12 x 2√3 = 10√36 = 10 x 6 = 60

400

2/√3

2√3/3

500

4/√2

2√2 because 4/√2 = 4√2/2 = 2√2

Pythagorean Theorem

100

What is the length of the missing side in the following right triangle?

5 feet

200

What is the length of the missing side in the following right triangle?

8 feet

300

What is the length of the missing side in the following right triangle? Simplify your answer as much as possible, no decimals!

5√3 feet

400

What is the length of the missing side in the following right triangle? Simplify your answer as much as possible, no decimals!

3√5 feet

500

What is the length of z in the diagram? (Hint: find the length of x first)

z = 12 because x = √(√2 x 8√2) = √16 = 4

So, 4² + (8√2)² = z²

16 + 128 = 144 = z² so z = 12

Lengths in Special Right Triangles

100

What is the length of x in the 45-45-90 triangle?

6√2

200

What is the length of x in the 30-60-90 triangle?

10 because 5 x 2 = 10

300

What is the length of y in the 30-60-90 triangle?

5√3 because the longer leg is √3 times longer than the shorter leg in a 30-60-90 triangle

400

What is the length of x in the 30-60-90 triangle?

10, because 10√3 divided by √3 is 10

500

What is the length of x in the 45-45-90 triangle? Simplify your answer as much as possible.

4√2, because 8/√2 = 8√2/2 = 4√2

Sine, Cosine, and Tangent Ratios

100

Name the ratios that sine, cosine, and tangent represent in a right triangle.

sine = opposite/hypotenuse

cosine = adjacent/hypotenuse

tangent = opposite/adjacent

200

What is cos θ equal to in the following right triangle? Simplify your answer.

3/5 or 0.6

300

What is tan θ equal to in the following right triangle? Simplify your answer.

4/3 or 1.33333333

400

What is the length of x in the following triangle?

6

500

My Squidward tapestry is 5 feet long across the bottom. If the angle of elevation from the bottom left corner to the top right corner is 30.96° then what is the length along the diagonal of the tapestry?

Roughly 5.83 feet because sin(30.96) = 5/x

so 0.8575/1 = 5/x, 0.8575x = 5, and x = 5/0.8575 = 5.83 feet

Random Trivia

100

What is my favorite color?

Orange

200

What are the three different subjects I taught this year? (all need to be correct to receive credit)

Geometry (three classes), Algebra 2 (one class), and Algebra 3 (one class)

300

How old am I?

26

400

What school did I teach at before working here?

Stemmers Run Middle School in Essex

500

Which of these colleges did I not attend for a period of time?

a) HCC

b) UMBC

c) Towson

d) UMD

d) UMD