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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.

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we will use trigonometry to solve a number of problems
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
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

the calculations
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

= 0.839  12

= 10.07 m

OPP

40

ADJ = 12

another example
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

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

the calculation
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

= 0.940  5

= 4.70 m

OPP

5

70

finding an angle
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-1 0.8 =36.9

another example8
Another example

SOHCAHTOA

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

OPP

HYP = OPP  Sin 59

= 3  0.8572

= 3.5 m

Sin x 

HYP

a further example
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?
calculations

SOHCAHTOA

Calculations

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

D

B

You need COS

ADJ = 1 .1

HYP AC = AB  cos 64

= 1.1 0.438 = 2.5 m

ADJ

Cos x 

How do you find the height BC?

HYP

finding the height
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
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
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?

the latitude
The Latitude

SOHCAHTOA

OPP

Use Tan

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)