5-Minute Check on Lesson 7-4a

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Transparency 7-5a
5-Minute Check on Lesson 7-4a

• Find x.
• 
  2.
• 3. Given an adjacent side and the hypotenuse,
  which trig function do you use?
• 4. Given an opposite side and the hypotenuse,
  which trig function do you use?
• 5. ?MNP is a 45- 45- 90 triangle with right
  angle P. Find NP if MN 20.
• 6. In
  the right triangle which trig function would you
  use to find CD with ?C?

x 17.43
x 53.14
32
x
x
10
6
33
cos
sin
10v2 14.14
C
D
Standardized Test Practice
37
5
cos
sin
tan
sec
E
A
C
B
D
C
Click the mouse button or press the Space Bar to
display the answers.
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Lesson 7-4b

• Right Triangle Trigonometry

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Trig Definitions
Opposite ---------------- Hypotenuse
S-O-H

• Sin (angle)
• Cos (angle)
• Tan (angle)

Adjacent ---------------- Hypotenuse
C-A-H
Opposite ---------------- Adjacent
T-O-A
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Ways to Remember

• S-O-H
• C-A-H
• T-O-A

Some Old Hillbilly Caught Another Hillbilly
Throwing Old Apples
Some Old Hippie Caught Another Hippie Tripping
On Acid
Extra-credit Your saying
5
Crash Trig Course
A
A
?
hypotenuse
hypotenuse
adjacent
opposite
?
C
C
B
B
opposite
adjacent
Whats Constant Side opposite right angle is
the hypotenuse What Changes Side opposite
the angle, ? Side adjacent to the angle, ?
In the triangle to the left AC is opposite of ?
and BC is adjacent to it In the triangle to
the right AC is adjacent to ? and BC is
opposite it
Left-most Triangle opposite side
AC sin ? -------------------
------ hypotenuse AB
adjacent side BC cos ?
------------------- ------
hypotenuse AB opposite
side AC tan ? -------------------
------ adjacent side BC
Right-most Triangle opposite side
BC sin ? -------------------
------ hypotenuse AB
adjacent side AC cos ?
------------------- ------
hypotenuse AB opposite
side BC tan ? -------------------
------ adjacent side AC
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Steps to Solve Trig Problems

• Step 1 Draw a triangle to fit problem
• Step 2 Label sides from angles view
• H hypotenuse
• O opposite
• A adjacent
• Step 3 Identify trig function to use
• Circle what values you have or are looking for
• SOH CAH TOA
• Step 4 Set up equation
• Step 5 Solve for variable

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Example 1
RememberSin 90 is 1 Cos 90 is 0
Tan 90 is undefined
SOH-CAH-TOA (Sin ? O/H, Cos ? A/H, Tan ?
O/A) ? is a symbol for an angle
sin2 ? cos2 ? 1 (from Pythagorean Theorem)
Example 1
When looking for an angle use the inverse of the
appropriate trig function (2nd key then trig
function on your calculator) 12 is opposite the
angle x and 8 is adjacent to it
opp, adj ? use tangent
tan x 12/8 x tan-1 (12/8)
x 56.31
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Example 2
RememberSin 90 is 1 Cos 90 is 0
Tan 90 is undefined
SOH-CAH-TOA (Sin ? O/H, Cos ? A/H, Tan ?
O/A) ? is a symbol for an angle
Example 2
When looking for a side use the appropriate trig
function (based on your angle and its
relationship to x, and your given side). 17 is
opposite of the angle and x is adjacent to it
opp, adj ? use tangent
tan 52 17/x x tan 52 17 x
17/tan 52 x 13.28
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Example 3
RememberSin 90 is 1 Cos 90 is 0
Tan 90 is undefined
SOH-CAH-TOA (Sin ? O/H, Cos ? A/H, Tan ?
O/A) ? is a symbol for an angle
Example 3
13 is the hypotenuse (opposite from the 90 degree
angle) and x is opposite from given angle
opp, hyp ? use sin
sin 47 x/13 13 sin 47 x 9.51
x
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Check Yourself

• You have a hypotenuse and an adjacent sideUse
  _______ Solve x ___
• You have an opposite and adjacent sideUse
  _______ Solve y ___
• You have an opposite side and a hypotenuseUse
  _______ Solve z ___

Cos
14.34
Tan
21.42
Sin
26.15
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Example 4
EXERCISING A fitness trainer sets the incline on
a treadmill to 7. The walking surface is 5 feet
long. Approximately how many inches did the
trainer raise the end of the treadmill from the
floor?
Step 1 Draw a triangle to fit problem Step 2
Label sides from angles view Step 3 Identify
trig function to use Step 4 Set up
equation Step 5 Solve for variable
S ? O / H C ? A / H T ? O / A
Opp y sin 7 --------
----- Hyp 60
Let y be the height of the treadmill from the
floor in inches. The length of the treadmill is 5
feet, or 60 inches.
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Example 4 cont
Multiply each side by 60.
Use a calculator to find y.
Answer The treadmill is about 7.3 inches high.
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Example 5
CONSTRUCTION The bottom of a handicap ramp is 15
feet from the entrance of a building. If the
angle of the ramp is about 4.8, how high does
the ramp rise off the ground to the nearest inch?
Answer about 15 in.
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Trig Practice
1) Identify what you are trying to find
(variable) Side or Angle 2) Relate given (opp,
adj, hyp, angle) to the variable 3) Solve for
variable
Side, x opposite 30 and 24 is the hyp ? sin 30
x/24 x 24 sin 30 12
Angle, x opposite 20 leg and 15 is adj leg ?
tan x 20/15 x tan-1 (20/15) 53.1
Side, x adjacent 60 and 30 is the hyp ? cos 60
x/30 x 30 cos 60 15
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Trig Practice cont
1) Identify what you are trying to find
(variable) Side or Angle 2) Relate given (opp,
adj, hyp, angle) to the variable 3) Solve for
variable
Side, x is hypotenuse and 12 is adj leg ? cos 45
12/x x 12/(cos 45) 12v2
Side, x opposite 49 and 13 is the hyp ? sin 49
x/13 x 13 sin 49 9.81
Angle, x is opposite 12 and 18 is hyp ? sin x
12/18 x cos -1 (12/18) 48.2
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Trig Practice cont
1) Identify what you are trying to find
(variable) Side or Angle 2) Relate given (opp,
adj, hyp, angle) to the variable 3) Solve for
variable
Side, x is adjacent 54 and 16 is opp ? tan 54
16/x x 16/(tan 54) 11.62
Angle, x is opposite 12 and adj to 10 ? tan x
12/10 x tan-1 (12/10) 50.2
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Summary Homework

• Summary
• Trigonometric ratios can be used to find measures
  in right triangles
• Identify what you are trying to find (variable)
  Side or Angle
• Relate given (opp, adj, hyp, angle) to the
  variable
• Solve for variable
• Homework
• pg 368, 18-21, 43-46, 61