Introduction to TrigonometryPart 2

Review: Adj / Opp / Hyp

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

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

Another tangent example

Find side B.

adj

opptan

CA = 6

25°

b

B87.1247.0

625tan

6

625tan

B

B

B

B

An application

65°

10m

You look up at an angle of 65° at the top of a tree that is 10m away

the distance to the tree is the adjacent side the height of the tree is the opposite side

4.21

14.210

65tan1010

65tan

opp

opp

opp

opp

Example 3

Angle b = 66.4 °Side A = 4 cmFind side C

C = x

a

66.4 °

B

A = 4

One last example…

Lucretia drops her walkman off the Leaning Tower of Pisa when she visits Italy

It falls to the ground 2 meters from the base of the tower

If the tower is at an angle of 88° to the ground, how far did it fall?

First draw a triangle

What parts do we have?We have an angleWe have the AdjacentWe need the oppositeSince we are working with

the adj and opp, we will use the tan formula

2m

88°

B

So lets calculate

Lucretia’s walkman fell 57.27m

2m

88°

B

27.57

264.28

288tan2

88tan

88tan

opp

opp

opp

opp

adj

opp

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?