1. Unit 5: Trigonometry
Final Exam Review

2. Topics to Include Pythagorean Theorem
Converse to the Pythagorean Theorem
Special Right Triangles
Trigonometry
Find a Missing Side Length
Find a Missing Angle Measure
Angle of Elevation and Depression

3. Pythagorean Theorem
The Pythagorean Theorem is used to find MISSING SIDE LENGTHS in RIGHT triangles.
The theorem: a2 + b2 = c2
a and b are the LEGS
c must be the HYPOTENUSE

4. Pythagorean Theorem Example a2 + b2 = c2 62 + 52 = x2 36 + 25 = x2
61 =𝑥
7.8 = x

5. Pythagorean Theorem
Now you try:

6. Converse to the Pythagorean Theorem
You can also use the Pythagorean Theorem to determine if a triangle is a RIGHT triangle
If you perform the Pythagorean Theorem and the equation is EQUAL, then the triangle IS a right triangle
If you perform the Pythagorean Theorem and the equation is NOT EQUAL, then the triangle is NOT a right triangle
If 𝒄 𝟐 < 𝒂 𝟐 + 𝒃 𝟐 , then the triangle is ACUTE
If 𝒄 𝟐 > 𝒂 𝟐 + 𝒃 𝟐 , then the triangle is OBTUSE

7. Converse to the Pythagorean Theorem
Example
Side lengths: 4, 12, 10
a2 + b2 = c2
= 122
= 144
116 = 144
Since 144 is greater than 116, the triangle is OBTUSE

8. Converse to the Pythagorean Theorem
Now you try:
1. Side lengths: 9, 40, Side lengths: 8, 7, 5

9. Special Right Triangles
There are 2 special right triangles that have side lengths that always have a common ratio. They are considered SHORT CUTS to the Pythagorean theorem.
45 – 45 – 90
30 – 60 – 90

10. Special Right Triangles
Example
X = U = 4
Y = 10 𝟐 V = 2 𝟑

11. Special Right Triangles
You Try
X = ________ X = ________ X = ________
Y = ________ Y = ________ Y = ________

12. Trigonometry
Trigonometry is used in order to find missing SIDE LENGTHS and missing ANGLE MEASURES in a right triangle
There are 3 trigonometric ratios
SINE
COSINE
TANGENT
In order to correctly find the missing side or angle, you must use the CORRECT ratio

13. Trigonometry SOHCAHTOA Sine Cosine Tangent OPPOSITE over HYPOTENUSE
ADJACENT over HYPOTENUSE
Tangent
OPPOSITE over ADJACENT

14. Trigonometry Example Which trig ratio would you use?
You would use TANGENT You would use SINE

15. Finding a Missing Side Length
To find a missing side length:
Determine which RATIO to use (sine, cosine, or tangent)
Set up the problem using the given ANGLE measure
Put a 1 under the trig ratio
CROSS multiply
Make sure your calculator is in DEGREE MODE

16. Find a Missing Side Length
Watch this video for an example on how to find a missing side length

17. Find a Missing Side Length
Now try this:

18. Finding a Missing Angle Measure
To find a missing angle measure:
Determine which RATIO to use (sine, cosine, or tangent)
Set up the problem using the given ANGLE measure
Use the INVERSE trig button in your calculator
Make sure your calculator is in DEGREE MODE

19. Find a Missing Angle measure
Watch this video for an example on how to find a missing angle measure

20. Finding a Missing Angle Measure
Now you try:

21. Angle of Elevation and Depression
Angles of Elevation and Depression are used in WORD PROBLEMS in order to find missing angles and side lengths
Angle of Elevation Angle of Depression
The Angle of Elevation and the Angle of Depression are ALWAYS EQUAL

22. Angle of Elevation and Depression
Now you try:
An escalator from the ground floor to the second floor of a department store is 110 ft long and rises 32 ft. vertically. What is the escalator’s angle of elevation?
From the top of a lighthouse 210 feet high, the angle of depression of a boat is 27. Find the distance from the boat to the foot of the lighthouse. The lighthouse was built at sea level.

23. ALL DONE