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Published byAbraham Ward Modified over 2 years ago

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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

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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

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Label the side that is the hypotenuse › This side is always across from the right angle A CB 3 4 5

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Label the side that is the hypotenuse › This side is always across from the right angle A CB 3 4 5hyp

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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

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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

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Label the leg adjacent to ∡A › This leg does touch ∡A - it helps to make ∡A. A CB 3 4 5hyp opp

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Label the leg adjacent to ∡A › This leg does touch ∡A - it helps to make ∡A. A CB 3 4 5hyp opp adj

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The tangent (tan) ratio involves only the legs of the triangle. › We will use opp and adj A CB 3 4 5hyp opp adj

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tan θ = A CB 3 4 5hyp opp adj opp adj

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tan A = = or 1.3333 A CB 3 4 5hyp opp adj opp adj 4 3 Our exampleRounded to four decimal places Exact fraction

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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

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sin θ = A CB 3 4 5hyp opp adj opp hyp

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sin A = = or 0.8 A CB 3 4 5hyp opp adj opp hyp 4 5 Our exampleDecimal formExact fraction

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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

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cos θ = A CB 3 4 5hyp opp adj hyp

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cos A = = or 0.6 A CB 3 4 5hyp opp adj hyp 3 5 Our exampleDecimal formExact fraction

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There’s a simple memory trick for these trigonometric ratios…

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s in θ = O pp / H yp c os θ = A dj / H yp t an θ = O pp / A dj

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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 20 21 29

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EXAMPLE 2 Find cosine ratios Find cos U and cos W. Write each answer as a fraction and as a decimal. cos U = adj. to U hyp = UV UW = 18 30 0.6000 cos W.

EXAMPLE 2 Find cosine ratios Find cos U and cos W. Write each answer as a fraction and as a decimal. cos U = adj. to U hyp = UV UW = 18 30 0.6000 cos W.

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