Transcript Trigonometry or SOHCAHTOA

Trigonometry:
SIN
COS
TAN
or SOHCAHTOA
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
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
x
ADJ
OPP
The Calculations
SOHCAHTOA
Suppose you measure the length of shadow
to be 12 metres. This is “ADJ”
Suppose the angle is 40
Which trig button is this?
Hint: TOA
OPP
Tan x  ADJ
OPP = Tan 40  12
= 0.839  12
= 10.07 m
OPP
40
ADJ = 12
Another example SOHCAHTOA
Joe buys a ladder which
extends to 5 metres.
However he would not feel safe
if the angle of the ladder
exceeds 70
How far up the wall would the
ladder extend at this angle?
5
OPP
What trig function is needed?
Hint:You know the HYP
You need SIN
70
The Calculation
SOHCAHTOA
The length of ladder is 5 m; this is “HYP”
OPP
Which trig button is this?
Hint: SOH
OPP = Sin 70  HYP
OPP = Sin 70  5
= 0.940  5
= 4.70 m
Sin x  HYP
5
70
OPP
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
Cos x = ADJ  HYP
x
ADJ = 4
Cos x = 4  5 = 0.8
In order to find the angle, use
”SHIFT COS” (or INV COS)
x = COS-1 0.8 =36.9
ADJ
Cos x 
HYP
Another example
SOHCAHTOA
Sue has a ladder which reaches 3m
up the wall when the angle is 59
HYP
How long is the ladder?
59
What trig function is needed?
Hint:You know OPP
You need SIN
HYP = OPP  Sin 59
= 3  0.8572
= 3.5 m
OPP
Sin x  HYP
OPP
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
• How long are the sides of the ladder?
• How high does the top reach?
2.2 m
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.
What trig button is needed?
You need COS
HYP AC = AB  cos 64
= 1.1 0.438 = 2.5 m
A
HYP
OPP
64
B
ADJ = 1 .1
ADJ
How do you find the height BC? Cos x  HYP
D
Finding the Height SOHCAHTOA
You could use TAN.
OPP
OPP
Tan x  ADJ
OPP = Tan 64  ADJ
= 2.050  1.1
= 2.26 m.
ADJ = 1 . 1
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...
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.
Which Trig. Button is this?
432 cms
The Latitude
SOHCAHTOA
Use Tan
OPP
Tan x  ADJ
Tan x = 400  432
= 0.9259
To find the angle x, you must do
“Shift Tan” (or Tan-1)
Tan-1 0.9259 = 42.8. (Your latitude is 42.8)