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

M May x A B C a b c Cah hypotenuse adjacent opposite A C B x cos x = Cah x = cos -1 ( 12 / 13 ) x = 22.6

M May cos 60˚ = cos 30˚ = cos 45˚ = cos 15˚ = cos 0˚ = cos 90˚ = cos 10˚ = cos 20˚ = cos 35˚ = cos 80˚ = cos 40˚ = cos x ˚ = 0.5 x ˚ = cos -1 (0.5) x ˚ = 60˚ cos x ˚ = 0.8 x ˚ = cos -1 (0.8) x ˚ = 36.9˚ cos x ˚ = 0.65 cos x ˚ = 0.12 cos x ˚ = 0.83 cos x ˚ = 0.21 cos x ˚ = 0.33 cos x ˚ = 0.47 cos x ˚ = 0.05 cos x ˚ = 0.72 x ˚ = cos -1 (0.65) x ˚ = cos -1 (0.12) x ˚ = cos -1 (0.83) x ˚ = cos -1 (0.21) x ˚ = cos -1 (0.33) x ˚ = cos -1 (0.47) x ˚ = cos -1 (0.05) x ˚ = cos -1 (0.72) x ˚ = 49.5˚ x ˚ = 83˚ x ˚ = 34˚ x ˚ = 78˚ x ˚ = 71˚ x ˚ = 62˚ x ˚ = 87˚ x ˚ = 44˚

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 is placed 2.7 metres from the step, will it be approved? 2.7 m 3 m x S o h C a h √√ cos x = x = cos -1 () x = x = 25.8˚ So since the angle lies between 20˚ and 26˚ the Council would approve the ramp.20˚ < 25.8˚ < 26˚ √

M May cos 30˚ = Use your calculator : cos 69˚ = cos 47˚ = cos 23˚ = cos 54˚ = cos 62˚ = cos 73˚ = cos 78˚ = cos 90˚ = cos 4˚ = cos x ˚ = x ˚ = cos -1 (0. 493) x ˚ = cos x ˚ = x ˚ = cos -1 ( ) x ˚ = cos x ˚ = x ˚ = cos -1 ( x ˚ = cos x ˚ = x ˚ = cos x ˚ = x ˚ = cos x ˚ = x ˚ = cos x ˚ = x ˚ = cos x ˚ = x ˚ =

M May cos 30˚ = Use your calculator : cos 69˚ = cos 47˚ = cos 23˚ = cos 54˚ = cos 62˚ = cos 73˚ = cos 78˚ = cos 90˚ = cos 4˚ = cos x ˚ = x ˚ = cos -1 (0. 493) x ˚ = cos x ˚ = x ˚ = cos -1 ( ) x ˚ = cos x ˚ = x ˚ = cos -1 ( x ˚ = cos x ˚ = x ˚ = cos x ˚ = x ˚ = cos x ˚ = x ˚ = cos x ˚ = x ˚ = cos x ˚ = x ˚ = ˚ ˚ 0.248) 75.6˚ cos -1 (0.478) 61.4˚ cos -1 (0.866) 30˚ cos -1 (0.234) 76.5˚ cos -1 (0.618) 51.8˚ cos -1 (0.476) 61.6˚

M May Remember The cosine of an angle is found using C a h cos x = x A djacent h ypotenuse x cos x = x = cos -1 (12/15) x = 36.9˚ S o h C a h T o a