### Video Transcript

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. What is the value of π΄π΅ cos π?

So the first thing we can do is add this angle. So itβs the angle π΄π·π΅. We know that itβs a right angle, 90 degrees. And we know that because weβre told that the line π΄π· is perpendicular, so therefore at right angles too the line π΅πΆ. So now, we have a right-angle triangle. And that triangle π΄π΅π· is useful because it includes the line π΄π΅ that weβre looking for.

Well, the first thing weβre gonna do is label our triangle. So the first label Iβm gonna put on is the hypotenuse because this is the longest side opposite the right angle. And then, we have the opposite. And thatβs because this is the side opposite the angle π. And then finally adjacent because this is the side thatβs next to the angle π, but also between π and the right angle.

So now, the next thing weβre gonna do is look at the trigonometric ratios. And we can do that because, as we said, weβre looking at a right-angle triangle. So to help us look at these, weβve got our memory aid, which is SOHCAHTOA. And if we take a look at the question, we can see that weβre looking for π΄π΅ cos π. So therefore, weβre 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, weβve got the adjacent and the hypotenuse. And Iβve 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 thatβs because thatβs the adjacent divided by the hypotenuse.

So now what we can do is multiply both sides of our equation by π΄π΅. And thatβs 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 weβre 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·.