Geometry Trig Lesson
Test 2
Algebra 2 textbook, Prentice Hall,
p.792
Objectives
Understand and use trigonometric
relationships of acute angles in
triangles.
Determine side lengths of right
triangles by using trigonometric
functions.
I can solve…
*Sin, Cos, Tan
*Sin -1, Cos -1, Tan -1
Example 1: Finding Trigonometric Functions
Find the values of the three (there are actually
six) trigonometric functions for θ.
Step 1 Find the length of the hypotenuse.
a2 + b2 = c2
Pythagorean Theorem.
70
θ
24
Example 1 answers
Step 2 Find the function values.
SIX
trigonometric function
• sine
• cosine
• tangent
• cosecants
• secant
• cotangent
Vocabulary
Example 2
Find the values of the six trigonometric
functions for θ.
Step 1 Find the length of the hypotenuse.
a2 + b2 = c2
Pythagorean Theorem.
80
θ
18
Example 2 answers
Step 2 Find the function values.
Example 3: Finding All Trigonometric Functions
Find the values of the six trigonometric
functions for θ.
Step 1 Find the length of the hypotenuse.
a2 + b2 = c2
Pythagorean Theorem.
70
θ
24
Example 3 answers
Step 2 Find the function values.
Application Assignment
• Due next class; Copy on your own paper; in
chart form (see below)
B
TRI ID
Ratio
Inverse Ratio
Trig ID
sin A
csc A
cos A
Sec A
tan A
cot A
sin B
csc B
cos B
cos B
tan B
cot B
C
A
Info:
AB = 25
CA = 16
CB = 9
I can solve for…
• Technology with trig functions
Clear calculators
Caution!
Make sure that your graphing calculator is set to
interpret angle values as degrees. Press
.
Check that Degree and not Radian is
highlighted in the third row.
first ALWAYS
Steps:
• 2nd 
• +
• 712 
• enter 
• clear MODE 
• using arrow keys twice down and once over right 
• enter 
• 2nd 
• MODE.
Example 1
Use a calculator to find tan
KEYSTROKES: TAN
Answer:
56
to the nearest ten thousandth.
ENTER
1.482560969
Example 2: Calculating Trigonometric Ratios
Use your calculator to find the trigonometric ratio. Round to the nearest
hundredth.
sin 52°
Caution!
Be sure your calculator is
in degree mode, not radian
mode.
sin 52°  0.79
Example 3
Use your calculator to find the trigonometric ratio. Round to the nearest
hundredth.
cos 30°
cos 30°  0.87
Example 4
Use your calculator to find each angle measure to the nearest degree.
a. tan-1(0.71)
tan-1(0.75)  35°
b. cos-1(0.05)
cos-1(0.05)  87°
c. sin-1(0.67)
sin-1(0.67)  42°
I can solve…
*Given degree and one side, solve for “ ? “
given
??
given
one piece of paper
note taking skills
Step
Example of step
Ex. 1: Finding Side Lengths of Right Triangles
Use a trigonometric function to find the value of x.
steps
What do I know from image, what do I need ?
opposite and hypotenuse
What trig function contains OPPOSITE and HYPOTENUSE ?
sin = opp
hyp
Fill in knowns and unknown, rearrange to solve for unknown
sin 30 = X
74
Example 1 cont.
the term I am
solving for is 74 sin 30 = X 74
74
isolated, HEY!
Calculator: 74  sin  30  enter
X = 37
EX. 2
Use a trigonometric function to find the value of x.
Steps:
1) What do I know ?
Example of step:
1) Hypotenuse & Opposite
2) What trig function contains opposite and
hypotenuse?
2) Sine = opp
3) Fill in knowns and unknowns
3) Sin 45 = X
4) Isolate what we are solving for
hyp
20
4) 20 sin 45
5) calculator
5) 14.14
Ex. 3
A surveyor whose eye level is 6 ft above the ground
measures the angle of elevation to the top of the highest
hill on a roller coaster to be 60.7°. If the surveyor is
standing 120 ft from the hill’s base, what is the height of
the hill to the nearest foot?
Ex. 4: Using Trigonometric Ratios to Find Lengths
Find the length. Round to the nearest hundredth.
BC?
***I can solve…
given
• Given two sides, solve for degree (inverse????)
given
??
***I can solve…
• Two degrees and one side give; solve for other side
given
given
given
????