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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 Toa hypotenuse adjacent opposite A C B 5 12 13 x tan x = 5 12 Toa x = tan -1 ( 5 / 12 ) x = 22.6

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M May tan 45˚ = tan 30˚ = tan 60˚ = tan 15˚ = tan 0˚ = tan 80˚ = 1 0.577 1.732 0.278 0 5.67 tan 85˚ = tan 88˚ = tan 35˚ = tan 87˚ = tan 22˚ = 11.43 28.64 0.700 19.08 0.404 tan x ˚ = 1 x ˚ = tan -1 (1) x ˚ = 45˚ tan x ˚ = 0.8 x ˚ = tan -1 (0.8) x ˚ = 38.7˚ tan x ˚ = 0.5 tan x ˚ = 0. 12 tan x ˚ = 0.83 tan x ˚ = 0.21 tan x ˚ = 0.33 tan x ˚ = 0.47 tan x ˚ = 0.05 tan x ˚ = 0.72 x ˚ = tan -1 (0.5) x ˚ = tan -1 (0.12) x ˚ = tan -1 (0.83) x ˚ = tan -1 (0.21) x ˚ = tan -1 (0.33) x ˚ = tan -1 (0.47) x ˚ = tan -1 (0.05) x ˚ = tan -1 (0.72) x ˚ = 26.6˚ x ˚ = 6.8˚ x ˚ = 39.7˚ x ˚ = 11.9˚ x ˚ = 18.3˚ x ˚ = 25.2˚ x ˚ = 2.9˚ x ˚ = 35.8˚

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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 lifts to top of the step 1.3 m high and is placed 2.9 metres from the step, will it be approved? 2.9 m 1.3 m x S o h C a h T o a √√ tan x = 1.3 2.9 x = tan -1 () 1.3 2.9 x = 24.14554196 x = 24.1˚ So since the angle lies between 20˚ and 26˚ the Council would approve the ramp.20˚ < 24.1˚ < 26˚ √√

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M May tan 30˚ = Use your calculator : tan 69˚ = tan 47˚ = tan 23˚ = tan 54˚ = tan 62˚ = tan 73˚ = tan 78˚ = tan 89˚ = tan 4˚ = tan x ˚ = 0.493 x ˚ = tan -1 (0. 493) x ˚ = tan x ˚ = 0.639 x ˚ = tan -1 ( ) x ˚ = tan x ˚ = 0.248 x ˚ = tan -1 ( x ˚ = tan x ˚ = 0.478 x ˚ = tan x ˚ = 0.866 x ˚ = tan x ˚ = 0.234 x ˚ = tan x ˚ = 0.618 x ˚ = tan x ˚ = 0.476 x ˚ =

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M May tan 30˚ = Use your calculator : tan 69˚ = tan 47˚ = tan 23˚ = tan 54˚ = tan 62˚ = tan 73˚ = tan 78˚ = tan 89˚ = tan 4˚ = tan x ˚ = 0.493 x ˚ = tan -1 (0. 493) x ˚ = tan x ˚ = 0.639 x ˚ = tan -1 ( ) x ˚ = tan x ˚ = 0.248 x ˚ = tan -1 ( x ˚ = tan x ˚ = 0.478 x ˚ = tan x ˚ = 0.866 x ˚ = tan x ˚ = 0.234 x ˚ = tan x ˚ = 0.618 x ˚ = tan x ˚ = 0.476 x ˚ = 0.577 2.605 1.072 0.424 1.38 1.88 3.27 4.705 57.29 0.070 26.2˚ 0.639 32.6˚ 0.248) 13.9˚ tan -1 (0.478) 25.5˚ tan -1 (0.866) 40.89˚ tan -1 (0.234) 13.2˚ tan -1 (0.618) 31.7˚ tan -1 (0.476) 25.5˚

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M May Remember The tangent of an angle is found using T o a tan x = x A djacent o pposite x 9 15 12 tan x = 9 12 x = tan -1 (9/12) x = 36.9˚

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M May S o h C a h T o a Hypotenuse x Adjacent Opposite sin x =cos x =tan x = Opposite HypotenuseAdjacenthypotenuse OppositeAdjacent S o h C a ha h T o a

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