Right Angle Triangle Trigonometry by tzf89584

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									                      Right Angle Triangle Trigonometry
                                                 90° Triangles

    Right Angle Triangle: Any triangle that has a 90° angle

    Hypotenuse: The side in a right angle triangle that is across from the 90° angle. It
    is always the longest side.

    Angle Sum: The sum of all three angles in any triangle is 180°

    Pythagorean Theorem
    When any two sides of a right angle triangle are known, the unknown side can be
    found by using the Pythagorean theorem:

                                                    a2 + b2 = c2
                                      Note: side “c” is always the hypotenuse

                                                  Example: A right angle triangle has one side
                                                  measuring 12cm and a hypotenuse measuring
                                                  13cm. Find the length of the third side.

                                                  Solution:
a                            c                                      a2 + b2 = c2
                                                                       a=?
                                                                     b = 12cm
                                                                     c = 13cm

                     b                                            x2 + 122 = 132
                                                                  x2 = 132 - 122
                                                                      x2 = 25
                                                                     x=
                                                                     x = 5cm




    Updated by: Jennifer Waugh, February 2010
                       Right Angle Triangle Trigonometry
Trigonometric Ratios
When an angle is given (other than the 90° angle) or when an angle needs to be
found we can use trigonometric ratios.

First we must learn how to label the sides of the triangle.



            Hypotenuse                                 Opposite
            (the longest side)                         (the side which does not
                                                       touch θ but does touch the
                                                       90° angle)

                                     θ
                           Adjacent
                           (the side which touches
                           both θ and the 90° angle)

The three ratios are:

cosθ =                                       sinθ =                       tanθ =

Note: remember to label your triangle first. Always label relative to the angle you
are interested in finding or that you have been given.

To remember to ratios you can use this mnemonic (memory aid):


                                            SOH CAH TOA
                                  SOH = sine, opposite over hypotenuse
                                 CAH = cosine, adjacent over hypotenuse
                                  TOA = tangent, opposite over adjacent

Updated by: Jennifer Waugh, February 2010
                                             Practice Question

                                                            Find the length of side “x”
                     12
                                               x



                38


                                                           Step 1: Label your sides
                                                           (Opposite, Adjacent and
                                                           Hypotenuse)
Hypotenuse          12
                                              x
                                              Opposite


               38
                    Adjacent
                                                             Step 2: Pick the ratio that
            sinθ =                                          contains two known values and
                                                            the unknown (x). Think SOH CAH
                                                            TOA.
            sin38 =                                         Step 3: Fill in your values and
                                                            solve for “x”. Hint: start by cross
            12 sin38 = x                                    multiplying.

            7.38 = x                                         Step 4: Type it into your
                                                            calculator to find x!




    Calculator Hints!
    Use the Sin/Cos/Tan button on your calculator if you know the angle. Use the Sin-1/Cos-
    1
      /Tan-1 if you want to find an angle.

    Always make sure your calculator’s mode is set to degree!



 Updated by: Jennifer Waugh, February 2010

								
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