Use sine because you have the measurements for opposite and need to find the hypotenuse.

- Set up a proportion Sine 30 = 5/x x= hypotenuse, 30 is the length of the opposite side of the right triangle.

- Take sine of 30 = .5

- Plug in .5 into the proportion for sine .5 = 5/x

- Cross multiply x = 5/.5 = 10 meters long.

A ramp has an angle of inclination of 30 degrees. It has a height of 5 meters, how long is the ramp?

Use tangent because you have the measurements for opposite over adjacent

- Set up a proportion Tangent 23 = x/45 x= opposite, 45 is the length of the adjacent side of the right triangle.

- Take Tan of 23 = .4244

- Plug in .4244 into the proportion for tangent .4244 = x/45

- Cross multiply x = 45 *.4244 = 19.101 meters

A hawk is sitting in a tree above a road. The hawk is watching a rodent that is 45 meters away from the tree and at an angle of 23 degrees. Calculate the height of the hawk.

35

opposite

adjacent

hypotenuse

10 units

X

When presented with a right triangle with missing angle measurements or side lengths, use trigonometric ratios in order to find the missing angle measures or side lengths.

A ratio is a comparison of one number to the size of another number. Therefore, a trig ratio tells you how one angle of a right triangle compares to the sides of the same triangle.

The trig ratios are used with right triangles to find side length and angle measures, but they can also be used as functions in equations.

The six trig ratios are sine, cosine, tangent, and their reciprocals, cosecant, secant, and cotangent.

Think of their names as shortcuts and time savers, instead of having to say, ”the ratio of the opposite over the hypotenuse,” one can just use “sine.”

Find the length of side x in the triangle** ABC ** below.

1. Decide which Trig Ratio to use. Ask yourself, what two sides am I using from the reference angle?

2. Set up the ratio. In this example you will use Tangent because we have the adjacent, but we need the opposite. Opposite and adjacent are the two sides of tangent.

Tan 35 = x/10 ( opposite/adjacent)

3. Use your calculator to find the Tangent, Cosine or Sine of the angle.

In this example take the Tangent of 35 which is .7002 (Type in Tan then 35 in your calculator OR 35 then Tan button)

4. Set up a proportion in order to cross multiply and solve for X

Sine Function |
sin(θ) |
Opposite / Hypotenuse |

Cosine Function |
cos(θ) |
Adjacent / Hypotenuse |

Tangent Function |
tan(θ) |
Opposite / Adjacent |