Trigonometry & Bearing
In this question angles are measured
Transcript
00:00This is unit 6, Trigonometry and Bearing, exercise 6.5.
00:04In this, we have a point E which is 200 meters away from a tower.
00:10You can call it a tower.
00:12After that, let's suppose that you mention that this is 200 meters and this is your tower.
00:28After that, there is a point B which is 80 meters away.
00:34If you have this point B and it is 80 meters away from the tower,
00:43then from here to here, let's suppose this is point O.
00:47When you are going from here to O to A, then how much distance do you have?
00:52It is 200 meters.
00:54Point B is 80 meters away from the tower.
01:01The distance between these two points is 80 meters.
01:05This is AB.
01:08If we subtract 80 meters from 200 meters, then we get 120 meters.
01:15Simply, BO is 120 meters.
01:23OC is your tower.
01:25Point A is on the ground which is 200 meters away.
01:31Point B is another point which is 80 meters away.
01:36It means that you will come backwards 80 meters.
01:40Now, the angle of elevation you have.
01:43What is angle of elevation?
01:46You are standing down and looking upwards.
01:49The angle of elevation you have at point A is alpha.
01:54He has described all this in the question.
01:58Angle of elevation of top of tower is alpha.
02:05The angle of elevation at point B is beta.
02:09You will take it here.
02:11This is beta.
02:14It is a simple question.
02:16You have a tower and point A on the ground.
02:20The distance between tower and point A is 200 meters.
02:23You have to find the height of the tower.
02:27The height of the tower is always straight and perpendicular.
02:30You have to find the angle of elevation at point B which is beta.
02:35First, we will align the statements.
02:38We need the height of the tower.
02:46That is OC.
02:51Secondly, we need the angle of elevation at point B.
02:57That is beta.
02:59Now, you will see that you have two triangles.
03:02We will solve both the triangles one by one.
03:05There is a big triangle.
03:06That is OCA.
03:08There is a small triangle.
03:09It is smaller comparatively.
03:10That is OCB.
03:12First of all, we will solve triangle OCA.
03:23In triangle OCA.
03:28Now, you will see that you have 10 alpha values.
03:35That is 2 by 5.
03:37We have 10 alpha values.
03:41We will use this value.
03:43What is 10?
03:45Through proper brush.
03:47Basically, you will have 10 of alpha.
03:50Perpendicular over hypotenuse.
03:59When the value of 10 alpha is given.
04:02That is 2 by 5.
04:04You will write 2 by 5 instead.
04:06Perpendicular is always a straight line.
04:09That is OC.
04:13This is hypotenuse.
04:15Where there are two lines, there is 90 degree angle.
04:18Opposite side is always hypotenuse.
04:22AC is the hypotenuse.
04:23So, this is going to be AC.
04:30Through proper brush.
04:34Hypotenuse will not come here.
04:35Base will come here.
04:40Base is from A to O.
04:44That is 200 meters.
04:47You will divide by 200.
04:50Because we can find one thing.
04:52We cannot find two things.
04:54We will do simple cross multiplication.
04:56Multiply 2 by 200.
04:58That is 400.
05:02Multiply 5 by OC.
05:05We have to find OC.
05:07Separate it.
05:09400 divided by 5.
05:13The value of OC is 80 meters.
05:19Perpendicular is 80 meters.
05:25This is the first part of the question.
05:28You have found the height of a tower.
05:31OC is basically height of a tower.
05:38When we find the height.
05:40Then we will find beta.
05:42Angle of elevation.
05:44Height of tower is finally 80 meters.
05:51Now you see.
05:52We have to find beta.
05:54That is angle of elevation.
05:56When we are standing at point B.
06:03I am going to choose another triangle.
06:06That is in triangle OCB.
06:14Again we will take tan.
06:16Because we need base and perpendicular.
06:18So you will have tan.
06:22Here it is tan alpha.
06:24Sorry tan beta.
06:26Perpendicular over base.
06:32Tan beta we do not know.
06:34We have to find.
06:38We have found the height of tower.
06:40That is 80 meters.
06:44Base is 120 meters.
06:46It is not necessary to take unit.
06:48Both units are same.
06:50When we divide them.
06:5280 divided by 120.
06:54We will get.
06:582 by 3.
07:01Now what you have to do.
07:03You have to find beta.
07:05You will find tan inverse.
07:102 by 3.
07:12Then you will get beta.
07:15That is 33.69.
07:19When you will do tan inverse 2 by 3.
07:21Then you will get beta value.
07:24That is 33.69 degrees.
07:29Here you will get beta value.
07:31This angle is 33.69 degrees.
07:36That's all.