Trigonometry

What is Trig?

Defined: Trigonometry is the Relationship between elements of a Triangle

Where can Trig be used in the construction business?

There are 6 elements of a triangle….

3 Sides and 3 Angles

A Right Triangle

Parts Include:

Right Angle

θ

Theta

θ

Opposite

Sides of the Triangle are:

θ

Opposite

Adjacent

θ

Opposite

Adjacent

Hypotenuse

θ

Opposite

AdjacentHypotenuse

The Ratios are Defined As…….

Sin θ= Opp Hyp

SOH

Cos θ= Adj Hyp

SOH CAH

Tan θ= Opp Adj

SOH CAH TOA

How Does it Work?

First it is important to lable the Triangle

CA

B

Sides = Upper Case Letters

a

b

c

Angles = Lower Case Letters

Once labeled we can find the dimensions of

unknown sides

?3

4

A²+ B²= C² 3²+ 4²= C²

53

?

A²+ B²= C² 3²+ B²= 5² B²= 5²- 3²

We can also Calculate the angles

53

4θ

b

c a

?

Using COS Find ‹bCOS=adj hyp

COS=3 5

b=cos

-1

3÷5 = 0.6

X 0.6 = 53.1º

53.1º