Question Video: Understanding the Cosine Ratio | Nagwa Question Video: Understanding the Cosine Ratio | Nagwa

Question Video: Understanding the Cosine Ratio Mathematics

In the given figure, πβ π΅π΄πΆ = 90Β° where π΄π· β₯ π΅πΆ. What is the value of π΄π΅ cos π?

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Video Transcript

In the given figure, the measure of angle π΅π΄πΆ is equal to 90 degrees, where the line π΄π· is perpendicular to π΅πΆ. What is the value of π΄π΅ cos π?

So the first thing we can do is add this angle. So itβs the angle π΄π·π΅. We know that itβs a right angle, 90 degrees. And we know that because weβre told that the line π΄π· is perpendicular, so therefore at right angles too the line π΅πΆ. So now, we have a right-angle triangle. And that triangle π΄π΅π· is useful because it includes the line π΄π΅ that weβre looking for.

Well, the first thing weβre gonna do is label our triangle. So the first label Iβm gonna put on is the hypotenuse because this is the longest side opposite the right angle. And then, we have the opposite. And thatβs because this is the side opposite the angle π. And then finally adjacent because this is the side thatβs next to the angle π, but also between π and the right angle.

So now, the next thing weβre gonna do is look at the trigonometric ratios. And we can do that because, as we said, weβre looking at a right-angle triangle. So to help us look at these, weβve got our memory aid, which is SOHCAHTOA. And if we take a look at the question, we can see that weβre looking for π΄π΅ cos π. So therefore, weβre gonna be interested in CAH, the part that deals with the cosine ratio. And what this tells us is that the cos of π is equal to the adjacent divided by the hypotenuse.

So therefore, if we take a look at our diagram, weβve got the adjacent and the hypotenuse. And Iβve circled these. And they are π΄π· and π΄π΅, respectively. So therefore, we can say that the cos of π is going to be π΄π· over π΄π΅. And thatβs because thatβs the adjacent divided by the hypotenuse.

So now what we can do is multiply both sides of our equation by π΄π΅. And thatβs because, first of all, it removes it from being the denominator removes the fractional element of our equation. But also, it will give us our π΄π΅ cos π that weβre looking for. So therefore, this would give us that π΄π΅ cos π is equal to π΄π·.

So therefore, we can say that the value of π΄π΅ cos π is going to be equal to π΄π·.

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