The Pythagorean theorem and how to use in trigonometry.

Welcome back to my class. This is a very easy question. We are asked to find the length of ad. Well, we can get this done using the Pythagorean theorem because we can actually find ad by Subtract the value of DB from the value of AB. Let's get to it immediately. Now, in this kind of question, what do we do? I'm going to disregard this line here, first of all. Yes, I need to ignore this line here, and I'm going to focus on angle ABC. So let me Do that immediately. So if I should focus on angle ABC, now we have this location and this Place. This is the hypotenuse. Okay, I'm moving too fast. First of all, the Pythagorean theorem. says that if you have a right-angled triangle, yes, if you have a right-angled triangle, This longest side is called the hypotenuse. Okay, the hypotenuse. Then let's call the remaining sides ab. The Pythagoras theorem says that a squared plus b squared equals b squared plus b The square of the longest side is equal to the sum of the squares of the other two sides. That is what the Pythagorean theorem states. So we are going to use this theorem to find the value we are looking for here. Okay, so first of all, as I said, we are going to ignore this particular line. That means I'm Focusing on triangle ABC. Then just draw it very small. You know my board is very small. So if I call this a, this b, and this c, this is four meters, this is a right angle, and this is six. meters. So I'm ignoring this particular one, this line because I'm ignoring it for now. So using I can easily get my line AB using the Pythagorean theorem. Yes, how? Remember what I just explained. My line AB squared, right? Let me do something like this. Line AB squared, this is line AB squared. plus this bc squared, that is four squared, is going to give us what? ac squared, that is six squared, right? Yes. Now, line AB squared plus four squared will give us 16 is equal to six squared. is 36. Now, line AB squared, line AB squared is equal to 36. Then this plus 16 will cross over to become minus 16, right? Minus 16. Now, what is line AB all squared equal to? We are going to have 20 here. That means that if I want to get the value of ab, that is from here to here, it's going To be what? The square root of 20. Yes, because for me to get ab, I need to take the square root of both. signs. So if I take the square root of both sides, I will have that my ab is going to be equal to What is the square root of? 20. The square root of 20 is 4.4721. So I'm going to write 4.47. 4.47 centimeters. So it means that line AB from here to here or from here to here will give What? 4.47 cm. Alright, now we are going to focus on triangle DBC, okay? Or BCD, Anyone. So let's focus on triangle BB CD. So if we draw it like this, this is our B, the right Angle, this is C, this is D. We have 5 meters here. Okay, sorry, this is in meters. We have 5. We have 4 meters here and 4 meters here. Alright, I can now find the length of line BD using the Pythagorean theorem. theorem as well. So how do we do that? This is our hypotenuse. So we know that this hypotenuse is equal to line BD, the line BD squared plus the line BC squared and BC is 4. So 4 squared, Okay? Using the Pythagorean theorem. Now we have that 25 is equal to line BD squared plus 16. because 4 squared is 16. Now, since we are looking for BD squared, this 16 we carry over so that only BD will remain here, okay? So we now have that BD squared is going to be equal 25 minus 16, because this plus 16 causes us to cross over and become minus 16. So it's going to be 25. minus 16. Alright, so we are going to have that bd squared, bd squared is equal to 25 minus 16, Therefore, our BD will be what? Square root of 9. Square root of 9, which will give us what? 3 meters. That means our BD is 3 meters, okay? Now remember that what we are looking for, What we are actually looking for is what? Ad. This ad and we can get ad from what? If we subtract db from ab, okay? We are going to have this one remaining, db, if we subtract it from ab. So we can now say that AD equals AB, right? This AD is going to be equal to the entire AB. Line AB minus line DB, line DB. This is point B, okay? Now what is our AD? That is what we are looking for. So line AD now is going to be equal to line AB. We have AB as 4.47 meters, 4.47 meters. minus 3 meters, minus 3 meters. So it's going to be what? 1.47 meters. If you followed me to this stage, please, this is the time you click on that notification bell and also click on the Follow the button so you'll be notified whenever I go live or post anything In this channel. Thank you so much for watching, and have a great day. Bye.