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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 5 12 13 x

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M May sin 30˚ = sin 60˚ = sin 45˚ = sin 75˚ = sin 90˚ = sin 10˚ = 0.5 0.866 0.707 0.966 1 0.174 sin 150˚ = sin 120˚ = sin 135˚ = sin 80˚ = sin 100˚ = 0.5 0.866 0.707 0.985 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 = 1.6 4 x = sin -1 () 1.6 4 x = 23.57818 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 ˚ = 0.584 x ˚ = sin -1 (0.584) x ˚ = sin x ˚ = 0.792 x ˚ = sin -1 (0. ) x ˚ = sin x ˚ = 0.153 x ˚ = sin -1 ( x ˚ = sin x ˚ = 0.305 x ˚ = sin x ˚ = 0.866 x ˚ = sin x ˚ = 0.234 x ˚ = sin x ˚ = 0.618 x ˚ = sin x ˚ = 0.476 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 ˚ = 0.584 x ˚ = sin -1 (0.584) x ˚ = sin x ˚ = 0.792 x ˚ = sin -1 (0. ) x ˚ = sin x ˚ = 0.153 x ˚ = sin -1 ( x ˚ = sin x ˚ = 0.305 x ˚ = sin x ˚ = 0.866 x ˚ = sin x ˚ = 0.234 x ˚ = sin x ˚ = 0.618 x ˚ = sin x ˚ = 0.476 x ˚ = 0.643 0.951 0.799 0.358 0.934 0.993 0.899 0.961 0.5 0.035 35.7˚ 792 52.4˚ 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 9 15 12 sin x = 9 15 x = sin -1 (9/15) x = 36.9˚

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STARTER x x In each triangle, find the length of the side marked x.

STARTER x x In each triangle, find the length of the side marked x.

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