7-2 Right Triangle Trigonometry

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7-2 Right Triangle Trigonometry

• Pull out those calculators!!!

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Absolutes

• Make sure the calculator is in degrees
• Scientific Press DRG button till you see
  DEG on the face
• Graphing Mode then toggle down and toggle
  left/right to degrees
• Make sure you know how to find sin/cos/tan of
  angles
• Scientific put in number, then press
  function
• Graphing Function, number, enter

3
Absolutes

• If you have a sine or cosine value and want to
  find the angle, you will use sin-1 or cos-1.
  These are the inverse functions.
• Remember the definition of inverse Put in
  the answer, get out the original (angle)

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• Everything will be based on the triangle shown
  below. As it is called Right Triangle Trig you
  can assume there is a right angle. We will
  always have the right angle in the same place.

B
c
a
A
C
b
Note B 42 means angle B 42.
5
Examples

• ?ABC is a right triangle with C 90?. Solve for
  the indicated part(s).
• A 42?, b 4 c ?
• 2. b 4, c 7 B ?

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Word Problems

• Before we do this, you need to understand 2
  standard phrases
• Angle of Elevation ________________
• ________________________________
• Angle of Depression _______________
• _________________________________

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Examples

• How tall is a tree whose shadow is 47 feet long
  when the angle of elevation is 49.3?

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4. One of the equal sides of an isosceles
triangle is 23 cm and the vertex angle is 43?.
How long is the base?
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8-1 Law of Cosines

• The first of 2 laws specifically for non-right
  triangles

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Notice Non-right Triangles

• We will be using this law when the information
  given fits
• _________________________________
• _________________________________

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B
a
c
A
C
b
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Area Formula
B
a
c
y
x
A
C
b
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Herons Formula

• Used to find areas of triangles when all sides
  are given (SSS)

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Example Find the area of the triangle
B
8
101
C
A
12
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Example Herons

• Given ?ABC with a 3, b 4 and c 5, find the
  area using Herons Formula.

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Example
1. a12 b5 c13 Find A
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8-2 Law of Sines

• The second of 2 laws specifically for non-right
  triangles

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Again Non-right Triangles

• We will be using this law when the information
  given fits AAS or ASA patterns.

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B
a
c
A
C
b
Law of Sines
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Examples

• Solve ?ABC if a 5, B 75º and
• C 41º.

A64º
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Example
Tom and Steve are 950 ft apart on the same side
of a lake. Rob is across the lake and he makes a
108 degree angle between Tom and Steve. Steve
makes a 39 degree angle between Tom and Rob. How
far is Tom from Rob?
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8-2 Law of Sines
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Try this

• Solve ?ABC if a 50, c 65 and A 57º
• What happened?

a
c
A
b
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a
c
c
a
A
A
b
b
c
a
c
a
A
b
A
b
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a
c
c
a
A
A
b
b
c
a
c
a
A
b
A
b
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How do we deal with this?

• When there are 2 triangles formed the B angles
  will be Supplementary. (Think Iso Triangle)

C
C
b
a
a
B
B
A
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What is the process to follow?

• If SSA triangle (given 1 angle)
• _______________________ (csinA)
• If only 1 ________________________
• If there are 2 triangles, ____________
• __________________________________________________
  ______________.
• __________________________________________________
  ______________

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ExampleSolve for B and c if A53 a12 and
b15
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Examples

• If you solved it regular first and get error or
  E as a solution that means that there is no
  triangle possible.
• Good one to remember!!

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2. Solve for ?ABC if c 65, a 60 and A
57º