5.4 Trig. Ratios Trigonometer Trigon- Greek for triangles Metric- Greek for Measure

Trig Ratios Trig. Ratios are used to find…… A missing side on a right triangle using one given side and an angle. Ex: 3cm

Trig Ratios Continued… Trig Ratios are also used to find… A missing angle on a right triangle using two given two sides. Ex. 3cm 4cm

Identifying sides of a triangle Sides of a triangle are referenced to the angle AdjacentHypotenuse Opposite

What if the angle is in the other corner? Sides are identified according to the reference angle. OppositeHypotenuse Adjacent

Trig Ratios Continued… Trig Ratios are constant values of right triangles that are based on the ratios of side measurements.

SOH CAH TOA

Trig Ratios 5cm13cm 12cm If you want to find the angle in degrees you can use your calculator or a chart

Finding the Angle in Degrees We already found this information Make sure your calculator is in degrees. Punch in 2 nd Function sin(.3846) Your answer should be degrees Punch in 2 nd Function cos(.9231) and your answer should still be degrees And the same thing if you do it for Tan

Finding the angle given 2 sides of a triangle 8cm12cm What are we going to use Sin, Cos or Tan? We have to use Sin WHY? We have to use sin because we have the opposite side and the hypotenuse

Finding the angles of a triangle 615 What ratio are we going to use sin cos or tan? We have to use cos because we have the adjacent side and the hypotenuse side.

Finding two angles given 2 sides What do we use sin, cos or tan when looking for the angles?

Find the missing Angle

Solutions Example #1 Example #2

Trig Ratios Part 2 Using Ratios to find the missing side. y X 15 You have to decide what formula you are going to use Sin, Cos or Tan Lets use Now solve for y by multiplying both sides by 15

Trig Ratios Part 2 Using Ratios to find the missing side. y X 15 You have to decide what formula you are going to use to solve for x Sin, Cos or Tan Lets use cos We have to move the x to the other side if we want to solve for X so to do this we must multiply both sides by x. The x’s will cancel on the right and now we must divide both sides by cos(45)

Solving for Sides VS Angles When solving for a side you have to use the function cos, sin, and tan When solving for an angle you need to use the inverse function (On your calculator you must push 2 nd function first)

Solving for a Side Find the missing side 12 x 30 y What are we going to use to find x SOH CAH TOA

Solving for a Side Find the missing side 12 x 30 y What are we going to use to find y SOH CAH TOA