Trigonometry
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Trigonometry. Right angled triangles. A triangle. Opposite and Adjacent are relative to the angle. The 4cm side is opposite to A The 6cm side is adjacent to A The 6cm side is opposite to B The 4cm side is adjacent to B. SOH CAH TOA Sine, Cosine & Tangent of an angle. SOH CAH TOA. SOH

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Trigonometry

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Trigonometry

Trigonometry

Right angled triangles


A triangle

A triangle


Opposite and adjacent are relative to the angle

Opposite and Adjacent are relative to the angle

  • The 4cm side is opposite to A

  • The 6cm side is adjacent to A

  • The 6cm side is opposite to B

  • The 4cm side is adjacent to B


Soh cah toa sine cosine tangent of an angle

SOH CAH TOASine, Cosine & Tangent of an angle


Soh cah toa

SOH CAH TOA

  • SOH

    • Some Old Houses

      • (Sine of angle =Opposite side / Hypotenuse)

  • CAH

    • Creak And Howl

      • (Cosine of angle = Adjacent side / hypotenuse)

  • TOA

    • Through Out Autumn

      • (Tangent of angle = Opposite side / adjacent side)


Toa soh cah

TOA SOH CAH

  • TOA

    • Tom’s Old Auntie

      • Tangent of angle = Opposite side / adjacent side

  • SOH

    • Sat On Him

      • Sine of angle =Opposite side / Hypotenuse

  • CAH

    • Cursing At Him

      • Cosine of angle = Adjacent side / hypotenuse


Soh cah toa1

SOH CAH TOA

  • SOH

S

O

H

Opposite side = sin (x) times hypotenuse

Hypotenuse = opposite side divided by sin (x)

Sin (x) = opposite side divided by hypotenuse


Soh cah toa2

SOH CAH TOA

C

A

  • CAH

H

Adjacent side = cos (x) times hypotenuse

Hypotenuse = adjacent side divided by cos (x)

Cos (x) = adjacent side divided by hypotenuse


Soh cah toa3

SOH CAH TOA

A

  • TOA

T

O

Opposite side = tan (x) times adjacent side

Adjacent side = opposite side divided by tan (x)

tan (x) = opposite side divided by adjacent side


Problems for trig

Problems for trig

A stage, is to be built for a concert, it has to be 2m high so the audience can see the show.

The equipment needs to be pushed up onto the stage. Health and safety rules say that a ramp must have a slope of no more than 15 degrees.

The crew need to work out how far away from the stage to start building the ramp.

m


Trigonometry

A stage, is to be built for a concert, has to be 2m high so the audience can see the show.

The equipment needs to be pushed up onto the stage. Health and safety rules say that a ramp must have a slope of no more than 15 degrees.

The crew need to work out how far away from the stage to start building the ramp.

m


Trigonometry

Put answer in context:

The ramp must start from at least 7.5m away from the stage


Trigonometry

From take-off, an aeroplane climbs at an angle of 20o. When the aeroplane has flown 10km, what height has it reached?

km

Distance from ground.


Looking for opposite distance from ground got hypotenuse must be sine formula triangle

Looking for opposite (distance from ground) got hypotenuse. Must be Sine formula triangle

km

Distance from ground.

Distance from ground = sin (20) x 10

= 3.42 km from the ground


Trigonometry

A plane flies 300km on a bearing of 132 0 from an airport. How far south and east is it from the airport. Give answer correct to 3 s.f.

North is always straight up your page for these questions..

Bearings are always measured from north around in a clockwise direction.


Trigonometry

Draw the problem and work out the angle at AThen choose which side you want to find first then choose the formula triangle to suit.


Distance south first looking for adjacent side therefore use cosine formula triangle

Distance South firstlooking for adjacent side therefore use cosine formula triangle


Distance east looking for opposite side therefore use the sine formula triangle

Distance East looking for opposite side therefore use the sine formula triangle


Ratio just means the number you get when you divide one number by another

Ratio just means the number you get when you divide one number by another

Similar shapes have the same angles – so they have the same angle ratios.

Sin(30) is always the same number no matter what size the opp or hyp

A

Cos(30) is always the same number no matter what size the adj or hyp

A1

A2

Tan(30) is always the same number no matter what size the opp or adj

B

C

C1

C2


Sine ratio sin x opp hyp

Sine ratioSin(x)=opp / hyp

4.3 / 8.42 = ?


To find the angle x when you know sin x use the calculator inverse sine function sin 1

To find the angle (x) when you know sin (x) use the calculator inverse sine function (sin-1)

  • Sin (x) = 0.86

    x = Sin-1 (0.86) = 59 0

  • Sin (x) = 0.35

    x = Sin-1 (0.35) = 21 0

    Sin (x) = 0.45 , what is x ?

    Sin (x) = 0.91, what is x?

27 0

66 0


Cosine ratio cos x adj hyp

Cosine ratiocos(x) = adj / hyp

Cos(30) = 0.86

16/18.46=?


To find the angle x when you know cos x use the calculator inverse cosine function cos 1

To find the angle (x) when you know cos (x) use the calculator inverse cosine function (cos-1)

  • Cos (x) = 0.86

    x = Cos-1 (0.86) = 31 0

  • Cos (x) = 0.35

    x = Cos-1 (0.35) = 70 0

    Cos (x) = 0.45 , what is x ?

    Cos (x) = 0.91, what is x?

63 0

24 0


Tangent ratio tan x opp adj

Tangent ratiotan(x) = opp / adj

Tan(30) =0.58

7.58 / 13 = ?


To find the angle x when you know tan x use the calculator inverse tangent function tan 1

To find the angle (x) when you know tan (x) use the calculator inverse tangent function (tan-1)

  • tan (x) = 0.86

    x tan(0.86) = 41 0

  • tan (x) = 0.35

    x = tan-1 (0.35) = 19 0

    tan (x) = 0.45 , what is x ?

    tan (x) = 0.91, what is x?

24 0

42 0


Trigonometry

A tourist lift to the top of a cliff travels 23m from ground to the top of the cliff. The height from ground to the top of the cliff is 20m what is the angle of elevation?

Choose a formula triangle

Sketch the problem

We have opposite and hypotenuse must be sine formula triangle


Looking for the angle bac work out the sine of the angle bac then use inverse sine to get angle

Looking for the angle BAC.Work out the sine of the angle BAC then use inverse sine to get angle.


Trigonometry

Health and Safety stipulates that a ladder held up at the side of a wall must have an angle of elevation between 700 and 800 to be considered safe. The height to be reached is 2.4m but the only ladder available is 4.9m will it be classed as safe?

Not safe


Find angles a and b we know all sides so any formula triangle will be ok to use

Find angles A and B?We know all sides so ANY formula triangle will be ok to use.


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