WEBVTT
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In the given figure, the measure of angle π΅π΄πΆ is equal to 90 degrees, where the line π΄π· is perpendicular to π΅πΆ.
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What is the value of π΄π΅ cos π?
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So the first thing we can do is add this angle.
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So itβs the angle π΄π·π΅.
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We know that itβs a right angle, 90 degrees.
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And we know that because weβre told that the line π΄π· is perpendicular, so therefore at right angles too the line π΅πΆ.
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So now, we have a right-angle triangle.
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And that triangle π΄π΅π· is useful because it includes the line π΄π΅ that weβre looking for.
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Well, the first thing weβre gonna do is label our triangle.
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So the first label Iβm gonna put on is the hypotenuse because this is the longest side opposite the right angle.
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And then, we have the opposite.
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And thatβs because this is the side opposite the angle π.
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And then finally adjacent because this is the side thatβs next to the angle π, but also between π and the right angle.
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So now, the next thing weβre gonna do is look at the trigonometric ratios.
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And we can do that because, as we said, weβre looking at a right-angle triangle.
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So to help us look at these, weβve got our memory aid, which is SOHCAHTOA.
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And if we take a look at the question, we can see that weβre looking for π΄π΅ cos π.
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So therefore, weβre gonna be interested in CAH, the part that deals with the cosine ratio.
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And what this tells us is that the cos of π is equal to the adjacent divided by the hypotenuse.
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So therefore, if we take a look at our diagram, weβve got the adjacent and the hypotenuse.
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And Iβve circled these.
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And they are π΄π· and π΄π΅, respectively.
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So therefore, we can say that the cos of π is going to be π΄π· over π΄π΅.
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And thatβs because thatβs the adjacent divided by the hypotenuse.
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So now what we can do is multiply both sides of our equation by π΄π΅.
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And thatβs because, first of all, it removes it from being the denominator removes the fractional element of our equation.
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But also, it will give us our π΄π΅ cos π that weβre looking for.
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So therefore, this would give us that π΄π΅ cos π is equal to π΄π·.
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So therefore, we can say that the value of π΄π΅ cos π is going to be equal to π΄π·.