1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Introduction Applied Mathematics Preliminary Stage 6

2 Click Hypotenuse OppositeAdjacent OppositeAdjacent Hypotenuseoppositeright-angle Hypotenuse – always opposite the right-angle. Oppositeoppositemarkedangle. Opposite – always opposite the marked angle. Adjacentnext-tomarked angle Adjacent – always next-to the marked angle.

3 a b c c Which is the Hypotenuse?

4 y z x x

5 p r q q

6 n g m Which is the Opposite? m

7 n g m n

8 n g m Which is the Adjacent? n

9 n g m m

10 θ Opposite θ : Adjacent θ : Hypotenuse: Hypotenuse :

11 θ Opposite θ : Adjacent θ : Hypotenuse: Hypotenuse : 5 4 3

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13 Hypotenuse Opposite Opposite Click Sin θ = OppositeHypotenuse θ θ Trig Ratios

Sin θ = OppositeHypotenuseP QR 5 Sin P = Sin R = 5 13 Trig Ratios

o m sin 30 o = m 6 6x x6 m = 6 x sin 30 o = 3 Use your Calculator! Trig Ratios Sin θ = OppositeHypotenuse

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17 Hypotenuse Adjacent Adjacent Click Cos θ = AdjacentHypotenuse θ θ Trig Ratios

Cos θ = AdjacentHypotenuseP QR 5 Cos P = 5 13 Cos R = Trig Ratios

o Cos θ = AdjacentHypotenusem cos 60 o = m 6 6x x6 m = 6 x cos 60 o = 3 Use your Calculator! Trig Ratios

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21 Opposite Adjacent Adjacent Click Tan θ = OppositeAdjacent θ θ Opposite Trig Ratios

Tan θ = OppositeAdjacentP Q R 5 Tan P = 12 5 Tan R = 5 12 Trig Ratios

o m Tan 30 o = m 6 6x x6 m = 6 x Tan 30 o ≈ 3.46 Use your Calculator! To 2 decimal places Trig Ratios Tan θ = OppositeAdjacent

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25 Trig Ratios How high is the Empire State Building in NYC 78 metres h 80 o tan 80 o = h 78 h =h = x78 78x tan 80 o = 442 metres

26 Trig Ratios How much rope is needed for a flying fox over the lake? d 40 m 60 o tan 60 o = d 40 h =h = x40 40x tan 60 o = 70 metres

27 S Some O Old H Hags C Can A Always H Hide T Their O Old A Age S Sin O Opposite H Hypotenuse C Cos A Adjacent H Hypotenuse T Tan O Opposite A Adjacent