• Suspects

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  • Mr. Hasmoore
• Topics
  • Percent of Change
  • Proportions
  • Trig Ratios
  • Weighted Averages

Trig ratios can only be used with right triangles.  On a right triangle the longest side is the side opposite of the right angle and it is called the hypotenuse.  The other two sides are called legs.  The Trig ratios that we will be using are Sine (sin), Cosine (cos), and Tangent (tan).

Consider the triangle below:  The capital letters represent the angles and the smaller case angles represent the sides.

            The hypotenuse side stays the same in a right triangle.  In this triangle, side b is the hypotenuse because it is opposite the right angle, B.  The other two sides, the legs are called either the Opposite or the Adjacent side.  In our triangle, side a is Opposite of angle A.  The only side left to label is side c, which is right next to angle A.  Side c is called the adjacent side.  For angle C, side c is the opposite and side a is the adjacent.  Angle B does not have the opposite or adjacent sides because it is the right angle.

For all triangles:                   For our triangle:

sine=        Sin A =a/b       Sin C = c/b

Cosine =     Cos A =c/b       Cos C = a/b

Tangent =       Tan A =a/c      Tan C = c/a

Let's try to solve for side c if given that side b = 10 and angle C = 30°

Using angle C we can set up our equation like this:

sin 30°= c/10  On a calculator find sin of 30 degrees (sin 30 degrees= .5) So,

.5 = c/10  Multiply both sides by 10

 5 = c.

The trick to trig ratios is knowing which function to use (sin, cos, or tan) and knowing how to set up your equations.

When given the opposite and hypotenuse use sine.

When given the adjacent and hypotenuse use cosine.

When given the opposite and adjacent use tangent.