# 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
(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

Hypotenuse)
Hypotenuse          12
x
Opposite

38
 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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