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Right Angled Triangles The key points Hypotenuse • The longest side of a right angled triangle • Always opposite the right angle Hypotenuse Pythagoras’ Theorem C (hypotenuse) A B • The two smaller sides, squared and added together equals the hypotenuse squared. • A2 + B2 = C2 • Only works for right angled triangles Find the length of ‘j’ 15cm hyp 12cm j • To find ‘j’, use P.T. • Label the hypotenuse. • 122 + j2 = 152 144 + j2 = 225 j2 = 81 j = 9 cm Any other sort of questions? Is this triangle right- angled? Hyp? 6cm 4cm 5cm • If it is then the hypotenuse is 6cm (longest side) and P.T. will work. • 42 + 52 = 16 + 25 = 41 62 = 36 so 42 + 52 = 62 P.T. does NOT work so no right angle So that’s it for right angled triangles? Unfortunately not Don’t forget trigonometry. (Worth big marks) 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. 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. 0 25 hyp adj opp Then pick your equation. Sin 0 = opp hyp Cos 0 = adj hyp Tan 0 = opp adj 0 is the Greek letter ‘theta’ which denotes an angle. 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. What? Find the value of ‘f’ ‘f ’ 10cm hyp opp 300 adj • 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 Find the value of angle BCA If I call angle BCA, ‘x’ A tan x = 4 / 10 = 0.4 4cm hyp so x = tan-1 0.4 opp B 10cm adj C x = 21.8o ( to 1 d.p.) How do I find an angle? obtuse reflex acute Find the value of 0 0 10cm hyp 5cm adj opp • 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) 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 I hope this helped I don’t want to have to say That’s all folks! The end