How to solve trigonometry involving Pythagoras theorem in a right angled triangle.

Welcome to my channel We are asked to find the length of BD, this BD here. Okay, we have to find the length of BD and we have to show that angle BCD Is equal to 90 degrees BCD. That means this angle, which we are asked to prove, is 90 degrees. Now this is a very simple thing, and it's under the topic of trigonometry. Okay, this is trigonometry. Alright. Now, how do we find this? I want to introduce you to something called the Pythagorean Theorem. So stay tuned and learn: this Pythagoras theorem states that when you have a right-angled triangle This is the right-angled triangle. Okay, this right angle, this right-angled triangle has three sides now: this side, this side, and this side. Okay. Now he's saying that this longest side, which is facing the right angle, is called the hypotenuse. Alright, then the hypotenuse, followed by the other two remaining sides. Let's call this one a and let's call this one b. Now the longest side, which is the hypotenuse. Let's call it h. We are told, according to Pythagoras, that this side squared—that is, h squared—is going to be equal to this a squared. Plus this b squared. Are you following me? Now this is what we're going to use to solve what we have here. All right. Now let's bring this home and relate it to what we have here when you look at this board now. You notice that this is a right-angled triangle; forget that they drew it like this. It's still a right angle, then this side that this right angle is facing This is the db that we are asked to find the bd What we are asked to find is actually the hypotenuse of the triangle now. We are going to use the Pythagorean theorem, which states that the square of the hypotenuse—the BD we are looking for— The bd we are looking for is going to be equal to this side squared, right, 3.3 squared, plus this side squared. Which is 5.6 squared. I hope you're following me. Alright, so we have that our bd squared is equal to 3.3 squared, which will give us 3.3 squared is 3.3 times 3.3. It will give us 10.89. Okay, so we have 10.89 here. Okay, plus 5.6 squared: 5.6 times 5.6. It's going to give us 31.36. 31.36 Now our BD squared Bd squared equals 10.89 plus 31.36. 10.89 plus 31.36 equals 42.25. We are going to have 42.25 So we have 42.25 As what is BD squared, but we are looking for BD. How do we now get BD? To clear this square, you need to take the square root of both sides. So you take the square root of both sides? Take the square root of what both? sides Now when you do that, the square root of bd squared is going to cancel this square. So you're left with only what bd is going to be equal to the square root of 42.25 If you've followed me to this point, it means you're actually enjoying what I'm doing. Alright, so I think it's time for you to click on that subscription button. So please subscribe to the channel if you haven't already, and then click on your notification bell So that you'll be notified anytime I upload a new video. Okay. All right, now BD_drawer is equal to the square root of 42.25 What is the square root of 42.25? We're going to get that soon. 42.25 is 6.5 So this is 6.5 Centimeters, so we have succeeded in obtaining the value of BD. So we have answered question a. Okay. Now, let us answer the second question, which says show that Angle BCD is 90 degrees; we should indicate that this angle is 90 degrees here. For us to show that this angle c here is 90 degrees That means this particular place is our hypotenuse once again, right? But it means that when we do this square and we add this square plus this square, just as we did here We are supposed to get the same answer that we obtained when using this particular angle to solve. Okay, so we'll do that once you're able to come up with the same answer we got here. That means the angle here is 90 degrees because that is the only way this angle can be 90 degrees. So let's go ahead and do that I'm claiming this right now So if you're not looking for this place, then from our perspective, that's the case. To prove that this is 90 degrees, that means our DB is our hypotenuse once again. Okay, so our db squared is going to be equal to 3.9 squared plus 5.2 squared. 5.2 squared. Okay. Now, what is 3.9 squared? 3.9 times 3.9 is going to give us 15.21 So what is this squared? 15.21 Plus 5.2 squared, Noble 5.2 times 5.2. I'm going to have 27.0 0.04 Okay. Now our DB squared is equal to April 27 plus 15.21 I'm going to have 42.25 42.25 Now to clarify this question, what are we going to do? We take the square root of both sides. So take square root of both sides They are going to have the square root of db. We give you the same thing; it's still going to give you line bd. Which we know is equal to the square root of what? 42.25 What is the square root of 42.25? The square root of 42.25 is 6.5 6.5 6.5 centimeters, and that is exactly what we obtained when we worked on this particular one. When we went, when we worked on this line using the first triangle, so that proved that yes. That our angle BCD is equal to us 90 degrees. Thank you so much for watching. Bye