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**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. A2 + B2 = C2 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 = 9 cm 15cm hyp 12cm j

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**Any other sort of questions?**

If it is then the hypotenuse is 6cm (longest side) and P.T. will work. = = 41 62 = 36 so = 62 P.T. does NOT work so no right angle Is this triangle right- angled? Hyp? 4cm 6cm 5cm

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**So that’s it for right angled triangles?**

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**Don’t forget trigonometry. (Worth big marks)**

Unfortunately not Don’t 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 Don’t 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? Find the value of ‘f’ We know the hypotenuse and want to find ‘f’ which is the opposite. We use sin 300 = f / 10 10 x sin 300 = f f = 5cm 10cm ‘f ’ hyp opp 300 adj

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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-1 0.4 x = 21.8o ( to 1 d.p.) A 4cm hyp opp B C 10cm adj

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How do I find an angle? obtuse reflex acute

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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 = 600 (cos-10.5) 10cm 5cm hyp adj opp

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**One more for luck! Find the value of ‘P’**

Sin 400 = P / 5 5 Sin 400 = P so P = 3.2cm (to 1 d.p.) hyp 5cm P cm opp 400 adj

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**I don’t want to have to say**

I hope this helped I don’t want to have to say

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That’s all folks! The end

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1 Trigonometry Basic Calculations of Angles and Sides of Right Triangles.

1 Trigonometry Basic Calculations of Angles and Sides of Right Triangles.

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