Introduction to TrigonometryPart 1

If you know 2 sides of a right triangle…

You can find the third side.A² + B² = C²B² = C² - A²A² = C² - B²

AC

B

a

b

If you know 2 angles…

You can find the missing angle.ma = 180 - (90 + mb)mb = 180 - (90 + ma)

AC

B

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

AC

B

b

adjhyp

opp

bC is always the hypotenuse

A is the adjacent side (next to the angle)

B is the opposite side (across from the angle)

LongestNext

Across

But if we switch angles…

Now let a be your reference angle

AC

B

a

opphyp

adja

C is always the hypotenuse

A is the opposite (across from the angle)

B is the adjacent (next to the angle)

LongestAcross

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 sinecos…short for cosinetan…short for tangent

So what are the formulas?

hyp

oppsin

hyp

adjcos SOH

adj

opptan

CAHTOA

Sin is Opposite over HypotenuseCos is Adjacent over HypotenuseTan is Opposite over Adjacent

If you need more help in memorizing…

Soh-Cah-ToaSome 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

adj

opptan

A C

B = 6

25°

b

80.2

647.0

625tan6

25tan

A

A

A

A

And one sin example

find the length of side A We have the angle and

the hyp, and we need the opp

hyp

oppsin

C = 20

25°

b

B

A 45.8

2042.0

2025sin20

25sin

A

A

A

A

What are the steps for doing one of these questions?

1. Label the sides

2. Choose SOH, CAH, or TOA

3. Solve the equation for the unknown value

4. Does the answer make sense?