8.3 The Tangent Ratio

1
8.3 The Tangent Ratio

• Essential Question
• How do you use tangent ratios to determine side
  lengths in triangles?

2
Tangent

• Your solution may be a fraction/decimal, so pay
  close attention when rounding.
• Tangent and the other trig ratios are used to
  estimate distances.

3

• To use the tangent ratio, you will need either a
  calculator or a textbook.
• On your calculator locate a tan button.
• To use this function
• Hit TAN
• You may need to include a (
• Next type in the fraction
• Include the ) and hit enter
• What if I dont have a calculator?
• Turn to page 769
• You can use this table for trig ratio problems.
• Lets practice using the table.

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Example 1 and Practice 1
5
Example 2 and Practice 2
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Practice Finding a side

• Find the value of the variable. Round to the
  nearest tenth.

7

• If you have the leg lengths use the tangent
  ratio to find the acute angle.
• If you have the acute angle use the inverse of
  the tangent ratio tan-1
• Locate the tan-1 button on your calculator.

8
Practice

• Find the value of the variable and round to the
  nearest tenth.

9
Practice

• What about problems like these?
• Try to solve and round to the nearest tenth.

10
Reflection

• How can the tangent ratio help with surveying
  land or applying to architecture/construction?

11
Summary

• Answer the summary question in detailed, complete
  sentences to make a paragraph.
• How do you use tangent ratios to determine side
  lengths in triangles?
• Create 2-4 study questions in the left column to
  correspond to the notes.