UNIT 5: TRIGONOMETRY
Final Exam Review
TOPICS TO INCLUDE
Pythagorean Theorem
Trigonometry
Find a Missing Side Length
Find a Missing Angle Measure
Angle of Elevation and Depression
Area of a Triangle (SAS)
Area of a Triangle (SSS)
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
PYTHAGOREAN THEOREM
Example
a2 + b2 = c2
62 + 52 = x2
36 + 25 = x2
61 = x2
61 = 𝑥
PYTHAGOREAN THEOREM
Now you try:
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
PYTHAGOREAN THEOREM
Example
A = 4, B = 10, C = 12
a2 + b2 = c2
42 + 102 = 122
16 + 100 = 144
116 = 144
NO, the triangle is not a right triangle
PYTHAGOREAN THEOREM
Now you try:
A = 9, B = 40, C = 41
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
TRIGONOMETRY
SOHCAHTOA
Sine
OPPOSITE over HYPOTENUSE
Cosine
ADJACENT over HYPOTENUSE
Tangent
OPPOSITE over ADJACENT
TRIGONOMETRY
Example
Which trig ratio would you use?
You would use TANGENT
You would use SINE
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
FIND A MISSING SIDE LENGTH
Watch this video for an example on how to find a
missing side length
FIND A MISSING SIDE LENGTH
Now try this:
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
FIND A MISSING ANGLE MEASURE
Watch this video for an example on how to find a
missing angle measure
FINDING A MISSING ANGLE MEASURE
Now you try:
1.
2.
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
ANGLE OF ELEVATION AND DEPRESSION
Now you try:
1. 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?
2. 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.
AREA OF A TRIANGLE (SAS)
You can use trigonometry to find the area of a non-right
triangle
Formula for SAS:
Example: 𝑨 =

𝟏
𝟐
𝑨=
𝟏
𝒂
𝟐
𝒃 𝒔𝒊𝒏𝑪
𝟓𝟖 𝟒𝟕 𝒔𝒊𝒏𝟏𝟏𝟎
A = 1280.8
AREA OF A TRIANGLE (SAS)
Try this one:
Find the area of the triangle
AREA OF A TRIANGLE (SSS)
Formula for SSS: 𝑨 = 𝒔(𝒔 − 𝒂)(𝒔 − 𝒃)(𝒔 − 𝒄)
S is the SEMIPERIMETER (which is HALF of the perimeter)
Example:
42+37+8
2
S=
= 43.5
𝑨 = 𝟒𝟑. 𝟓(𝟒𝟑. 𝟓 − 𝟒𝟐)(𝟒𝟑. 𝟓 − 𝟑𝟕)(𝟒𝟑. 𝟓 − 𝟖)
A = 122.7cm2
AREA OF A TRIANGLE (SSS)
Now try this:
Find the area of the triangle
ALL DONE