Geometry Final Exam Review 3 - Right Triangles

Geometry Final Exam Review 3 - Right Triangles

By Tiffany Madison

How to simplify a radical

Multiple Choice

Simplify: $$\sqrt[]{48}$$  

• $$3\sqrt[]{6}$$  

• $$4\sqrt[]{3}$$  

• $$6\sqrt[]{6}$$  

• 14

Multiple Choice

Simplify: $$\sqrt[]{192}$$  

• $$8\sqrt[]{5}$$  

• $$3\sqrt[]{3}$$  

• $$8\sqrt[]{3}$$  

• $$4\sqrt[]{2}$$  

Multiple Choice

• A
• B
• C
• D

How to Solve

1. Determine what side is missing.

2. Plug in what you know into the equation.

3. Simplify the equation.

4. Solve for the missing side.

5. If needed round to the nearest tenth!

Multiple Choice

Determine the length of the missing side.

• 7

• 8

• 17

• 23

Multiple Choice

Find the value of x.

• 7
• 8
• 9
• 10

Classifying Right Triangles

• If c² = a² + b² --> right triangle

• If c² < a² + b² --> acute triangle

• If c² > a² + b² --> obtuse triangle

Multiple Choice

• Acute

• Obtuse

• Right

• Not a Triangle

Multiple Choice

• Acute

• Obtuse

• Right

• Not a Triangle

Multiple Choice

• Acute

• Obtuse

• Right

• Not a Triangle

Multiple Choice

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

• 4√2
• 4
• 8
• 4√3

Multiple Choice

Find the missing side lengths.

• a = 4, b = 4
• a = 4, b = 2√2
• a = 2√2,  b = 4
• a = 4, b = 4

Multiple Choice

What is the length of u and v in this 30-60-90 triangle?

• u = 8 v = 4√3
• u = 4√2 v = 8
• u = 16 v = 8
• u = 4√3 v = 8

Multiple Choice

Find a.

• 3

• $$3\sqrt{3}$$

• 6

• $$\sqrt{3}$$

Multiple Choice

Find the ratio for the given triangle.

• $$\frac{12}{5}$$  

• $$\frac{12}{13}$$  

• $$\frac{5}{12}$$  

• $$\frac{13}{12}$$  

Multiple Choice

Find the ratio for the given triangle. 

• $$\frac{12}{5}$$  

• $$\frac{5}{12}$$  

• $$\frac{13}{12}$$  

• $$\frac{12}{13}$$  

Using Trig Ratios to Solve for Missing Side Lengths

Trig ratios can be used to find missing side lengths.

Multiple Choice

Solve for x.

• 31.2

• 5.6

• 14.6

• 6.2

Multiple Choice

Solve for x.

• 17.2

• 27.1

• 8.3

• 30.9

Using Trig Ratios to Solve for Missing Angles

Remember to use the inverse function

Multiple Choice

Find the measure of the indicated angle (?) round to the nearest tenth.

• 9.4
• 55.2
• 20.15
• 19.4

Multiple Choice

A ladder is leaning against a wall. The foot of the ladder is 6.5 feet from the wall. The ladder makes an angle of 74^𝑜 with the level ground. How high on the wall does the ladder reach?

Which of the following is the correct diagram for the problem?

Multiple Choice

Which scenario describes the picture shown?

• A 5 foot ramp is 8 feet away from a building.  What is the angle that the ramp makes with the ground?
• A 5 foot ramp leans against an 8 foot structure.  What is the angle that the ramp makes with the ground?
• An 8 foot ramp leans
  against a building 5 feet away.  What angle does the ramp make with the ground?
• A 5 foot man is 8 feet away from a building.  What is the angle of elevation?