8.5 The Tangent Ratio

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8.5 The Tangent Ratio
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• Trigonometry ? Greek word for triangle
  measurement
• We will work only with right triangle
  trigonometry
• Tangent is a ratio of the lengths of the legs of
  a right triangle.
• Formula

Opposite leg
A
Adjacent leg
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The mathematical abbreviation for tangent is tan.
Whatever my angle I am dealing with then follows
immediately afterwards.
Finding the tangent ratio of the given angles.
C
13
9
B
A
5
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• The tangent (function/ratio) explains the
  relationship between an angle and the sides
  opposite and adjacent that angle.
• We can use the tangent function to find missing
  side lengths and to find missing angle
  measurements.

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The tangent of an angle, depends only on the
angles measurement.

• Most calculators will allow you find the tangent
  of any angle measurement. For example, if you
  have a TI-83/84 you can simply type in tan(45)
  and it will spit out its value. Do not worry
  right now what that value means. If you have one
  of these calculators you must make sure that your
  mode is in degrees. Check by pressing the MODE
  button and going down and highlighting DEGREE.
• Other calculators like the small TI-30x you have
  to push the 45 then find the tan function and
  press it.
• So depending on your calculator you need to
  understand its order of operations.
• The calculators that you will be using for the
  OGT allow you to simply type in tan(45) just like
  the TI-83/84.

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With your calculator find the following

• tan 45
• tan 34

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Sometimes you will be given the following

• tan __?__ 5/8
• If you are given what the tangent should be, then
  you need to solve to find out what the angle
  measurement is. The function on your calculator
  is called the inverse tangent.
• On a TI-84 we just press that button and then
  plug in 5/8

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• Find the following angle measurements.
• tan__?__ 2/3
• tan__?__15/22
• tan __?__ 1
• tan __?__ .466308

These 2 actually tell you what the leg lengths
are. The ones with decimals have already done
the division and converted to ratio into a
decimal.
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Find the value of y to the nearest tenth.
y
15
21
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Find z.
z
78
61
14
y
9
23
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Now we want to find an angle measurement given 2
known sides. We will use the tan-1 button
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Find this angle measurement
13
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Now we want to find an angle measurement given 2
known sides.
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Find this angle measurement
13 3
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Now we want to find an angle measurement given 2
known sides.
Find this angle measurement
6
8
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• A person at window W, 40 feet above street level,
  sights points on a building directly across the
  street. H is chosen so that WH is horizontal. T
  is directly above H, and B is directly below H.
  By measurement, mltTWH61 and mltBWH 37. How
  tall is the building across the street?

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Homework pg. 308 7-18, 21-24, 27

• If looking for a leg, you will just use the tan
  button.
• Remember to find an angle measurement you use
  tan-1

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