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∆ABC has three angles… › ∡C is a right angle › ∡A and ∡B are acute angles We can make ratios related to the acute angles in ∆ABC A CB 3 4 5
Let’s start with ∡A ! We need to label the three sides of the triangle with their positions relative to ∡A. A CB 3 4 5
Label the side that is the hypotenuse › This side is always across from the right angle A CB 3 4 5
Label the side that is the hypotenuse › This side is always across from the right angle A CB 3 4 5hyp
Label the leg opposite from ∡A › This leg doesn’t touch ∡A at all – it is across the triangle from ∡A. A CB 3 4 5hyp
Label the leg opposite from ∡A › This leg doesn’t touch ∡A at all – it is across the triangle from ∡A. A CB 3 4 5hyp opp
Label the leg adjacent to ∡A › This leg does touch ∡A - it helps to make ∡A. A CB 3 4 5hyp opp
Label the leg adjacent to ∡A › This leg does touch ∡A - it helps to make ∡A. A CB 3 4 5hyp opp adj
The tangent (tan) ratio involves only the legs of the triangle. › We will use opp and adj A CB 3 4 5hyp opp adj
tan θ = A CB 3 4 5hyp opp adj opp adj
tan A = = or A CB 3 4 5hyp opp adj opp adj 4 3 Our exampleRounded to four decimal places Exact fraction
The sine (sin) ratio involves the hypotenuse and one of the legs. › We will use opp and hyp A CB 3 4 5hyp opp adj
sin θ = A CB 3 4 5hyp opp adj opp hyp
sin A = = or 0.8 A CB 3 4 5hyp opp adj opp hyp 4 5 Our exampleDecimal formExact fraction
The cosine (cos) ratio also involves the hypotenuse and one of the legs. › We will use adj and hyp A CB 3 4 5hyp opp adj
cos θ = A CB 3 4 5hyp opp adj hyp
cos A = = or 0.6 A CB 3 4 5hyp opp adj hyp 3 5 Our exampleDecimal formExact fraction
There’s a simple memory trick for these trigonometric ratios…
s in θ = O pp / H yp c os θ = A dj / H yp t an θ = O pp / A dj
Find sin X, cos X, and tan X › Remember to label hyp, opp, & adj › Find answers as both fractions and decimals (rounded to four places) Z YX
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