1. Trigonometry: SIN COS TAN or
SOHCAHTOA

2. We will use Trigonometry to solve a number of problems
How could you find the height of this flagpole?
Measure the length of the shadow, and the angle of elevation x
SOHCAHTOA

3. First identify the sides of the triangle
SOHCAHTOA
The longest side is called the…
Hypotenuse.
The side opposite is called the…
Opposite.
The remaining side is the…
Adjacent
HYP
OPP x
ADJ

4. The Calculations SOHCAHTOA
Suppose you measure the length of shadow to be 12 metres. This is “ADJ”
Suppose the angle is 40
OPP
Which trig button is this?
Hint: TOA
Tan x 
ADJ
OPP = Tan 40  12
=  12
= m
OPP
40
ADJ = 12

5. Another example SOHCAHTOA 5
Joe buys a ladder which extends to 5 metres.
However he would not feel safe if the angle of the ladder exceeds 70 5
How far up the wall would the ladder extend at this angle?
What trig function is needed?
Hint:You know the HYP
OPP
70
You need SIN

6. The Calculation SOHCAHTOA The length of ladder is 5 m; this is “HYP”
OPP
Which trig button is this?
Hint: SOH
Sin x 
HYP
OPP = Sin 70  HYP
OPP = Sin 70  5
=  5
= 4.70 m 5
OPP
70

7. Finding an Angle SOHCAHTOA
The base of this triangle is 4 cms, the hypotenuse is 5 cms.
How can you find the angle x?
Which trig button is this?
Hint: _AH
HYP = 5
OPP
Use COS…..BUT x
Cos x = ADJ  HYP
Cos x = 4  5 = 0.8
In order to find the angle, use ”SHIFT COS” (or INV COS)
ADJ = 4
ADJ
Cos x 
HYP
x = COS =36.9

8. Another example SOHCAHTOA HYP = OPP  Sin 59 = 3  0.8572 = 3.5 m
Sue has a ladder which reaches 3m up the wall when the angle is 59
How long is the ladder?
HYP
OPP
59
What trig function is needed?
Hint:You know OPP
You need SIN
HYP = OPP  Sin 59
= 3 
= 3.5 m
OPP
Sin x 
HYP

9. A further example SOHCAHTOA
A stepladder has the shape of an isosceles triangle. The distance between its feet is 2.2 m.
The angle the legs make with the horizontal is 64
64
2.2 m
How long are the sides of the ladder?
How high does the top reach?

10. Calculations SOHCAHTOA
First you need to work with a right angled triangle. C
AC is the hypotenuse in ABC.
AB is the adjacent, length 1.1 m.
HYP
OPP
What trig button is needed?
64 A B D
You need COS
ADJ = 1 .1
HYP AC = AB  cos 64
= 1.1 = 2.5 m
ADJ
How do you find the height BC?
Cos x 
HYP

11. Finding the Height SOHCAHTOA You could use TAN. Tan x 
OPP
OPP
Tan x 
ADJ
OPP = Tan 64  ADJ
=  1.1
= 2.26 m.
ADJ = 1 . 1

12. A Final example SOHCAHTOA
The participants in a TV series are ‘dumped’ on an uninhabited island somewhere…
One of the problems they have to solve is to find the location of their island.
The first step is to find the latitude - essentially, this determines how far north (or south) you are.
This can be done by measuring the angle the North Star makes with the horizontal. (At the North Pole, it is overhead!)
It would be quite feasible to make a rudimentary protractor, but this might not be very accurate. SO...

13. The Solution SOHCAHTOA
The idea is to line up the star with a suitable tall object, whose height you can measure. To keep things simple, let’s suppose you have a 4m pole.
Also suppose that when you line up your eye, the North Star appears behind the top of the pole, and your eye is 432 cms from the pole as measured along the horizontal.
What sides in the triangle do you know?
400 cms
The Opposite and Adjacent.
432 cms
Which Trig. Button is this?

14. The Latitude SOHCAHTOA Use Tan Tan x = 400  432 = 0.9259
OPP
Use Tan
Tan x 
ADJ
Tan x = 400  432 =
To find the angle x, you must do “Shift Tan” (or Tan-1)
Tan = 42.8. (Your latitude is 42.8)