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TrigonometryTrigonometry Right angled triangles

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A triangle

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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

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SOH CAH TOA Sine, Cosine & Tangent of an angle

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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)

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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

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SOH CAH TOA SOH SOH Opposite side = sin (x) times hypotenuse Hypotenuse = opposite side divided by sin (x) Sin (x) = opposite side divided by hypotenuse

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SOH CAH TOA CAH CA H Adjacent side = cos (x) times hypotenuse Hypotenuse = adjacent side divided by cos (x) Cos (x) = adjacent side divided by hypotenuse

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SOH CAH TOA TOA TO A Opposite side = tan (x) times adjacent side Adjacent side = opposite side divided by tan (x) tan (x) = opposite side divided by adjacent side

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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

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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

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Put answer in context: The ramp must start from at least 7.5m away from the stage

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

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Looking for opposite (distance from ground) got hypotenuse. Must be Sine formula triangle Distance from ground. Distance from ground = sin (20) x 10 = 3.42 km from the ground km

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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.

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

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

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

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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. A A1A1 A2A2 B C1C1 C2C2 C Sin(30) is always the same number no matter what size the opp or hyp Cos(30) is always the same number no matter what size the adj or hyp Tan(30) is always the same number no matter what size the opp or adj

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Sine ratio Sin(x)=opp / hyp 4.3 / 8.42 = ?

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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

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Cosine ratio cos(x) = adj / hyp Cos(30) = 0.86 16/18.46=?

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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

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Tangent ratio tan(x) = opp / adj Tan(30) =0.58 7.58 / 13 = ?

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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

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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? Sketch the problem Choose a formula triangle We have opposite and hypotenuse must be sine formula triangle

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

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Health and Safety stipulates that a ladder held up at the side of a wall must have an angle of elevation between 70 0 and 80 0 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

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

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