Introduction to Trigonometry Part 1

If you know 2 sides of a right triangle… You can find the third side. A² + B² = C² B² = C² - A² A² = C² - B² b C A a B

If you know 2 angles… You can find the missing angle. ma = 180 - (90 + mb) mb = 180 - (90 + ma) b C A a B

What if you know one side & one angle and you want to find the missing sides? Now you need to use trigonometry! First we have to learn some vocabulary.

Some vocabulary: The hypotenuse (hyp) is the longest side of the triangle – it is always across from the right angle The opposite (opp) is the side directly across from the reference angle The adjacent (adj) is the side next to the reference angle

A picture always helps… Let b be your reference angle A is the adjacent side (next to the angle) b C A B is the opposite side (across from the angle) B b Next C is always the hypotenuse hyp Longest adj opp Across

But if we switch angles… Now let a be your reference angle A is the opposite (across from the angle) C A a B is the adjacent (next to the angle) B Across C is always the hypotenuse hyp Longest opp a adj Next

Let’s practice… label each side relative to the reference angle.

Trigonometry uses ratios of the sides There are three sets of ratios for any triangle sin…short for sine cos…short for cosine tan…short for tangent

So what are the formulas? Sin is Opposite over Hypotenuse Tan is Opposite over Adjacent Cos is Adjacent over Hypotenuse SOH CAH TOA

If you need more help in memorizing… Soh-Cah-Toa Some old horse Caught another horse Taking oats away. Some old horse Caught another horse Trotting on asphalt.

Calculating a side if you know the angle you know a side (adj) and an angle (25°) we want to know the opposite side b C A 25° B = 6

And one sin example find the length of side A We have the angle and the hyp, and we need the opp b C = 20 A 25° B

What are the steps for doing one of these questions? Label the sides Choose SOH, CAH, or TOA Solve the equation for the unknown value Does the answer make sense?