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M May Trigonometry Measures of triangle Remember Angles of triangle add to 180˚ hypotenuse opposite adjacent Right-angled triangle

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M May x A B C a b c Soh hypotenuse adjacent opposite A C B x

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M May sin 30˚ = sin 60˚ = sin 45˚ = sin 75˚ = sin 90˚ = sin 10˚ = sin 150˚ = sin 120˚ = sin 135˚ = sin 80˚ = sin 100˚ = sin x ˚ = 0.5 x ˚ = sin -1 (0.5) x ˚ = 30˚ sin x ˚ = 0.8 x ˚ = sin -1 (0.8) x ˚ = 53.1˚ sin x ˚ = 0.65 sin x ˚ = 0.12 sin x ˚ = 0.83 sin x ˚ = 0.21 sin x ˚ = 0.33 sin x ˚ = 0.47 sin x ˚ = 0.05 sin x ˚ = 0.72 x ˚ = sin -1 (0.65) x ˚ = sin -1 (0.12) x ˚ = sin -1 (0.83) x ˚ = sin -1 (0.21) x ˚ = sin -1 (0.33) x ˚ = sin -1 (0.47) x ˚ = sin -1 (0.05) x ˚ = sin -1 (0.72) x ˚ = 41˚ x ˚ = 7˚ x ˚ = 56˚ x ˚ = 12˚ x ˚ = 28˚ x ˚ = 3˚ x ˚ = 46˚

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M May The angle a ramp makes with the horizontal must be 23 ± 3 degrees to be approved by the Council. If this ramp is 4m long and lifts up a height of 1.6 m, will it be approved? 1.6m 4m x S o h √√ sin x = x = sin -1 () x = x = 23.6˚ So since the angle lies between 20˚ and 26˚ the Council would approve the ramp.20˚ < 23.6˚ < 26˚

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M May sin 40˚ = Use your calculator : sin 72˚ = sin 53˚ = sin 21˚ = sin 69˚ = sin 83˚ = sin 64˚ = sin 106˚ = sin 150˚ = sin 2˚ = sin x ˚ = x ˚ = sin -1 (0.584) x ˚ = sin x ˚ = x ˚ = sin -1 (0. ) x ˚ = sin x ˚ = x ˚ = sin -1 ( x ˚ = sin x ˚ = x ˚ = sin x ˚ = x ˚ = sin x ˚ = x ˚ = sin x ˚ = x ˚ = sin x ˚ = x ˚ =

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M May sin 40˚ = Use your calculator : sin 72˚ = sin 53˚ = sin 21˚ = sin 69˚ = sin 83˚ = sin 64˚ = sin 106˚ = sin 150˚ = sin 2˚ = sin x ˚ = x ˚ = sin -1 (0.584) x ˚ = sin x ˚ = x ˚ = sin -1 (0. ) x ˚ = sin x ˚ = x ˚ = sin -1 ( x ˚ = sin x ˚ = x ˚ = sin x ˚ = x ˚ = sin x ˚ = x ˚ = sin x ˚ = x ˚ = sin x ˚ = x ˚ = ˚ ˚ 0.153) 8.8˚ sin -1 (0.305) 17.8˚ sin -1 (0.866) 60˚ sin -1 (0.234) 13.5˚ sin -1 (0.618) 38.2˚ sin -1 (0.476) 28.4˚

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M May Remember The sine of an angle is found using S o h sin x = x o pposite h ypotenuse x sin x = 9 15 x = sin -1 (9/15) x = 36.9˚

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