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Right AngledTriangles Right Angled Triangles The key points

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Hypotenuse The longest side of a right angled triangle Always opposite the right angle Hypotenuse

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Pythagoras Theorem The two smaller sides, squared and added together equals the hypotenuse squared. A 2 + B 2 = C 2 Only works for right angled triangles

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Find the length of j To find j, use P.T. Label the hypotenuse j 2 = j 2 = 225 j 2 = 81 j = 9 cm 15cm 12cm j hyp

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Any other sort of questions? If it is then the hypotenuse is 6cm (longest side) and P.T. will work = = = 36 so = 6 2 P.T. does NOT work so no right angle Is this triangle right- angled? 4cm 5cm 6cm Hyp?

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So thats it for right angled triangles?

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Unfortunately not Dont forget trigonometry. (Worth big marks)

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Key trigonometry facts Trigonometry links the size of the angles to the length of the sides. Only works in right angled triangles. Can be used to find either a length or an angle Dont forget to check that your calculator is working in degrees.

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Help! Label the sides of your triangle Hypotenuse (hyp) - opposite the right angle. Opposite (opp) - opposite the angle you know or want to find. Adjacent (adj) - the remaining side.

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Then pick your equation. Sin 0 = opp Cos 0 = adj Tan 0 = opp hyp hyp adj 0 is the Greek letter theta which denotes an angle.

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But which one should I use? If you are trying to find an angle, work out which two sides you know and use the formula that contains them both. To find a missing side, work out which side you want to find and the side you know and then use the formula which contains both.

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What? We know the hypotenuse and want to find f which is the opposite. We use sin 30 0 = f / x sin 30 0 = f f = 5cm 10cm f adj 30 0 opp hyp Find the value of f

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Find the value of angle BCA If I call angle BCA, x tan x = 4 / 10 = 0.4 so x = tan x = 21.8 o ( to 1 d.p.) B A C 10cm 4cm hyp adj opp

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How do I find an angle? obtuse acute reflex

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Find the value of 0 Label the sides. We know adj and hyp so must use cos cos 0 = 5 / 10 cos 0 = 0.5 so 0 = 60 0 (cos ) 0 10cm opp 5cm adj hyp

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One more for luck! Find the value of P Sin 40 0 = P / 5 5 Sin 40 0 = P so P = 3.2cm (to 1 d.p.) 5cm P cm 40 0 opp adj hyp

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I hope this helped I dont want to have to say

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Thats all folks! The end

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