Transcript Lesson 9-1 & 9-2: Trigonometry of Right Triangles (Sine, Cosine

Lesson 9-1 & 9-2:
Trigonometry of Right Triangles
(Sine, Cosine, Tangent)
SOH-CAH-TOA
Using Trigonometry in Right
Triangles
• Be able to find the ________,
Opposite
________,
Adjacent
and __________
sides from an angle
Hypotenuse
________
Adjacent
Hypotenuse
________
Opposite
_______
Opposite
________
Adjacent
• __________
& _________
depend on
Opposite
Adjacent
where you start!
Next to
• Adjacent means “______”
STAYS
• Hypotenuse ______
hypotenuse
Trig Ratios
Opposite
Adjacent
• Use _________,
_________,
and
Hypotenuse
____________
to set up ratios (fractions)
• These ratios are related to the size of
Angle
the__________
• Three Trig Functions
Sine (sin)
____________
Cosine (cos)
____________
Find them on your
calculator!
Tangent (tan)
____________
ALWAYS talking about an angle!!!
Sin, cos, tan are _________
Trig Ratios
opposite
sin  
hypotenuse
adjacent
cos  
hypotenuse
opposite
tan  
adjacent
► SOH-CAH-TOA
____________
A
300
2
3
B
1
1
sin
sin 
AA
2
3
2
1
tan
tan
AA
3
cos
cos
AA
C
Using calculator to find angles
From the previous slide, solve for angle A:
So:
1
sin A 
2
1
sin sin A  sin  
2
1  1 
A  sin  
2
1
1
A  30
1
sin 30 
2
0
Inverse of
sin is sin-1
sin
1
1
 30 0
2
0
angle
fraction/decimal
Sin of an ___________
gives the ___________________
fraction/decimal
angle
Sin-1 of an ____________________
gives the ___________
Using Trig
• Finding a missing side
missing
1. Label the angle, given side, and ___________
side (x)
2. Draw a _____________
stick figure by the angle
adjacent
3. Identify the given and missing sides using ___________,
______________,
and _________________
opposite
hypotenuse
SOH-CAH-TOA
4. Choose 1 of the 3 equations from: _________________
5. Fill in equation with numbers and x
proportion (sin, cos, tan can be over “1”)
6. Solve using a __________
• Finding a missing angle given 2 sides
1. Follow steps 1 – 5 above, then
inverse
2. Solve for the angle by using the __________
trig function
with the fraction/decimal →
5
sin A 
8
A  sin 1
5
8
Find sin L, cos L, tan L, sin N, cos N, and tan N.
Express each ratio as a fraction and as a decimal.
Answer:
EXERCISING A fitness trainer sets the incline on a
treadmill to
The walking surface is 5 feet long.
Approximately how many inches did the trainer raise
the end of the treadmill from the floor?
Let y be the height of the treadmill from the floor in inches.
The length of the treadmill is 5 feet, or 60 inches.
Proportion: Multiply sin 70 by 60, divide by 1 if you want to
KEYSTROKES: SIN
7
X
60 ENTER 7.312160604
Answer: The treadmill is about 7.3 inches high.