00:00 Hello, my name is Oyase, Sunday I'll be taking you mathematics for JSS3 and we have

00:20 an interesting topic for today, which is trigonometry, an aspect of our measurement and geometry.

00:29 And the question is what to be the focus for the class? The focus for the class is to be

00:35 able to identify sine, cosine and tangent of an acute angle. Two soft problems on application

00:43 of trigonometry ratio to finding distance and length. How do you apply trigonometry

00:49 ratio to finding distance and length? And three apply trigonometry ratio in solving

00:56 what problems? Boops straight up. Now trigonometry ratio is applied on a triangle. You see that

01:09 a triangle has three sides. So the right angle triangle has three sides. At least the right

01:19 angle triangle it has a three sides. The longest side is called the hypotenuse. It has the

01:26 longest of the side. The sides facing the angle, there's always an angle theta a, the side

01:33 facing the angle is called the opposites. Why the down part is called the adjacent? So

01:40 in trigonometry we live at the three sides of the triangle. So we say the trigonometry

01:45 is derived from the Greek word trigonometry. Means triangle and metro means measure. So

01:51 we'll be measuring triangles. But it's a bunch of mathematics that studies relationship

01:55 between the size length and angles of the triangle. So let's both for trigonometry we

02:02 would be liberating the sides. So like I said the longest side is called the hypotenuse.

02:07 The sides facing the angle is the opposite. Then the downside is called the adjacent. You

02:14 could see it's well. Good. Move on. Now trigonometry to the relation of angle theta. This theta

02:22 can be illustrated in three patterns. We have the same, we have the cause and we have the

02:29 tan which is popularly called soca tua. Now how do we arrive at that? Peking the first

02:36 one. Let's do an analysis of this triangle on the board. Now we have sine, sine theta.

02:47 Sine theta is opposite over adjacent. We say opposite over sine theta opposite sorry over

02:58 hypotenuse. That's the longest side. Opposite over hypotenuse. Sine theta, opposite over

03:04 hypotenuse. So when you pick out the sine out you have your x, you have your o and you have

03:11 your h. Now we move to the cause. We move to cause theta. Cause theta gives us adjacent

03:22 over hypotenuse. Adjacent over hypotenuse. Now move it out the same way I did. I have the

03:34 c out, you have the a out and you have the h out. Now going forward we have the last called

03:44 the tan. Tan theta. Tan theta gives us opposite over adjacent. I have opposite over adjacent.

03:58 Now move it out like I said. Move out the t. Move out the o and move out the a. So when

04:05 you combine the three you could add the abbreviation as soca tua. Opposites over hypotenuse for

04:14 sine. Adjacent over hypotenuse for cause and opposite over adjacent for tan. You could

04:23 apply to solve a right angle triangle. Now let's pick an example one. So we will have

04:31 an idea of the o analysis and its application. The diagonal below shows a right angle triangle

04:37 with sides of length 16, 12 and 20 units. The two acute angles are labeled alpha and beta.

04:50 I'm in the value of tan beta for the triangle given that the answers as a simplified fraction.

04:58 Now what we just simply do at this point. You have a right angle triangle given. This

05:05 is a right angle triangle given in this form. Let's have a right angle triangle given drawn

05:10 down. The longer side which is the hypotenuse. The longer side is given to be what? 20. This

05:17 opposite is 12. Opposite to the angle. The angle we have in the air is what? Angle beta.

05:27 Why the downside is 16? So if we follow two with a soca tua and we have to find tan theta.

05:36 Then tan beta. Tan beta is what? Remember from the ones we have that is also what? Opposite

05:48 over what? Adjacent. And so what's your opposite over adjacent? What's your opposite

05:55 over adjacent? Your opposite is what? Your opposite already given to be what? 12. Don't

06:01 forget. That will give you what? 12. What's your adjacent? 16. So in a simplified fraction.

06:09 I have three here. Four can go. Successfully. Four here. Four in here will give me three and

06:17 four into 16 will give me four. So I will just say my tan beta will give me three over

06:25 four. Now I could just try it out. Okay. What will be my sign? My sign beta? From the angle

06:36 ambient. Remember? Remember your sign. Go back to have your sign. What's your sign?

06:42 A sign is opposite. What's your opposite? Your opposite here. You have as what? The opposite

06:48 here is what? 12. And what's your hypotenuse? Your hypotenuse is the longer side which is

06:54 20. So you could also continue to go with your sign and your go along the way. So you could

07:01 just try it out. A mixture of the application makes it a bit easier to apply. Oh, I have it

07:08 this way and this other way. So it makes it a bit easier to what? Apply. Like I said, the

07:13 time in the value of the tan theta where we have the pq, the pr divided by pq which is

07:20 12 by 16 and equal to 3 over 4. 4 the time. Let's take another a bit of I.I example. The person

07:32 stands at point A. Looking at a bed sitting at the top of a tree at point B. Stand at point A,

07:42 looking at the bed sitting at the top of the tree at point B. The height of the tree is S

07:49 m. Point A is 7.14 m away from the foot of the tree. And the angle of incination that is upward

08:01 from the horizontal to the top is 35 degree. Calculate the height of the tree. That is the X.

08:09 Calculate the height of the tree and put your answer in two decimal places. Look at the tree.

08:18 A is the standing position. B is where the bed is. C to B is the height which you are looking for.

08:28 And that is the side which is 1447.14 m. Cest is the representation. Once you can represent it out,

08:40 it is easier to solve. Now you simply look at this. What are the size that are given?

08:47 We are given the opposite and we are given the adjacent. So even before start solving,

08:52 ability to be able to identify the sides gives you an idea on how to solve. It is the first step

08:59 in solving. Identifying the number of sides that you are being given in a particular triangle.

09:05 Because now we have two sides. The other questions might give you multiple of other sides. So

09:11 identify the ones that are given. The ones facing the angle is the opposite. So we have opposite

09:17 over adjacent. Adjacent. That means our pattern is not given. So if I have opposite over adjacent,

09:24 carefully. What is opposite over adjacent? Opposite over adjacent. Who give us time? Remember,

09:31 time is opposite over adjacent. So write down the definition of the ratio in terms of the lines,

09:37 in relation to A and the side that you need to calculate for your BC. The side you need to calculate

09:44 for your BC. We are looking for the BC. And so I would just simply say apply application. That's

09:51 for question number two. I would simply say my tan. My tan theta or tan theta is opposite. Opposite

10:01 opposite is representable word BC over adjacent. That's AC. Now going forward, moving forward,

10:10 I have what's my tan. I would just simply say my tan 35 degree. My tan 35 degree from this.

10:19 My tan 35 degree would just simply give me 35 degree would give me what's my BC. My BC is what?

10:30 X from the diagram. My BC is X. What's my AC? My AC is 7.14. Once you can identify the side,

10:40 that I give you. If you did it again, once you can identify the side that I give you in the triangle,

10:47 it is easier to solve a trigonometry questions. So once I have this, what do I need to do?

10:54 I would simply cost multiply. Now when I multiply, make this of our one multiply in this form,

11:01 base this. So I could say my X is equal to I would have 7.14. 7.14 multiplied by

11:14 tan 35. 7.14 multiplied by tan 35. Now you could take your calculator and press tan 35. You have

11:30 your answer will give you 4.994. 4.9994. But we have been told to random to the nearest word decimal.

11:51 So half 4.9. To the 9 decimal, you have 9 added up. This up to 1. Added up just 1. Added up 1.

11:59 So added up to 5. That gives 4. That gives us 5. So I have X equal to the nearest. That give us 5 meter.

12:07 If you see it very well, it becomes more easier to do. It becomes more easier. Once you identify

12:15 the sides, the major challenge in a trigonometry is the sides. Once you can identify the sides,

12:22 you can take off any challenge that is based on trigonometry. Provided you know your sign,

12:27 your sign, provided in New York, your cost, and you know your tan. Once you know your sign,

12:32 cost, and tan, you could pick up any trigonometry questions and it's a good to go. So now into the

12:39 aspect of the evolution. After solving those two, we do the individual evolution where you

12:44 expected to rule apply. Now a person standing at a point A, this, a sign at a point A,

12:53 and looking up at a satellite dish at the top of a building, looking up at a satellite dish at the

13:04 top of a building, looking up, satellite dish at the top of a building at a point B. The height of

13:15 the building is 6 meter. Now the height is given. In the first person we solved, the height wasn't

13:21 given. We had to find the height. The height here, the totalness of the building is given. 6 meter.

13:29 Now, 6 meter. The line of the side, line of side distance from point A to the top of the building,

13:38 that's point B, is X. The line of side, the line at which it looks at the top of the building is X,

13:45 which is unknown. Now, and the angle of inclination, that is from the horizontal to the top of the

13:52 building is 62 degree, calculate the line of side. The line of side simply means the longest line,

13:59 which is the hypotenuse. To the top of the building at X, run up your answer to the decimal place.

14:07 Tastic diagram, you're looking for your X. What is given? Your given is, you have your opposite,

14:14 that is given, then your hypotenuse. So, I could read, you could know, the particular one to apply.

14:21 They are designed to cause all the time. Thank you very much. We've come to the end of the class.

14:27 My name is Oyase Sunday.