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Trigonometry
Maths and Fun together
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7/9/2024
In this question Trigonometric ratios are used
Category
📚
Learning
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00:00
This is unit 6, Signometry and Bearing, exercise 6.5.
00:04
Two men on opposite sides of a tree in line with it, they observe that angles of elevation
00:09
of top of tree are 30 degrees and 60 degrees.
00:14
The height of our tree is 15 meters, we have to find the distance between them.
00:18
Simple question hai, sabse pehle aapke paas ek straight line aa jayegi, that is 15 meters.
00:24
Ye height ho gayi tree ki.
00:26
Ab aapke paas do log hai.
00:28
Dono tree ke opposite directions peh kadein, jo door khada hai, let's suppose yaha pe
00:34
ek person khada hai, to uska angle of elevation chota hoga.
00:38
Angle of elevation ye hota hai ki agar aap neeche khade ho aur aap upar ki taraf dekh
00:43
rahe ho.
00:44
Doosra person jo ke iske kareeb khada hai tarakht ke, uska angle of elevation zyada
00:49
hoga.
00:50
Humme malum karna hai ki ye jo do log hain, inke darmayan kitna faasla hai.
00:55
Aap is point ko T name kar do aur isko C kar do.
00:59
Ab aapke paas do triangles hai.
01:03
A, C, T, B, C, T.
01:07
Aap dono ko solve karoge.
01:13
Ab aap dekho ki aap is pe kya lagaoge, 10 through proper brush.
01:19
So, 10, 30 degrees, perpendicular aur base aapke paas kya jayega 80.
01:33
10 kya hota hai aapke paas, ki aapka perpendicular aur base aata hai.
01:39
Through proper brush aapka perpendicular aajayega aur aapka base aajayega.
01:43
To base aapke paas 80 hai.
01:45
To 30 ki value kar hum calculator se calculate karein, to humme milta hai 0.57 into 7, 15, 80.
01:57
Ab aap kya karoge, aap cross multiplication kar sakte ho.
02:01
Aap iske neeche 1 laga do.
02:03
Simply iske saath multiply aajayega aur 15, 1 ke saath multiply aajayega.
02:07
Jis bhi cheez ko humne malum karna hota hai, hum usko isolate karte hai.
02:17
To 80 humare paas ho jayega, 15 divided by 0.577.
02:23
So, final value jo aapke paas 80 ki aayegi, that is going to be 25.99 meters.
02:31
Abhi humne kya kiya hai, humne chhute wale triangle ko solve kiya hai.
02:35
10 humne lagaya hai yaha pe.
02:37
This is perpendicular aur 80 humare paas base hai.
02:40
10, 30 ki degree ki value aapne paas 0.577 hai.
02:44
Cross multiplication karein.
02:46
80 ko aapne malum karna hai.
02:48
Jisko hum malum karte hain, usko isolate karte hain, uski value nikaal rahte hain.
02:52
Ab hum aachenge bhi doosar triangle ke liye, that is in triangle BCT.
03:00
Isme bhi aapka 10 lagega.
03:04
Tan theta kya hota hai aapke paas?
03:06
Perpendicular over base.
03:08
Perpendicular humesha humari straight line hogi.
03:12
Yaha pe aapke paas tan ka jo angle use ho raha hai, that is 60 degrees.
03:17
Perpendicular aapke paas 15 meters hai.
03:22
Aur base aap B, T likhto, T, B likhto, dono tara se same baat hai.
03:27
Tan 60 degrees ki value aapke paas aa chahiye ki, square root 3.
03:35
Ye table aap chaho to yaad bhi kar sakto.
03:37
Yaha simple calculator se, jab aap tan 60 ki value nikaal hoge, that will be square root 3.
03:43
Hum cross multiplication karenege.
03:47
Square root 3 multiply ho chahega T, B ke saath.
03:50
Aur 15, 1 ke saath multiply hoge, 15 hi aayega.
03:54
T, B aapke paas barabar ho chahega.
03:57
15 divided by square root 3.
04:02
That is going to be equal 8.66 meters.
04:07
Ab finally aap kya karoge?
04:09
Aapke paas A, T aa gaya, that is 25.99 meters.
04:15
Aapke paas T, B aa gaya, that is 8.66 meters.
04:20
In dono ko plus karlo, to aapke paas A, B aa chahega.
04:23
Jo ki hum is question mein maloom karna tha.
04:26
That is, A, B is equal to 34.65 meters.
04:34
Aani ki aapke paas jo faasla hai, wo basically 34.65 meter ka hai.
04:39
Hum A, T maloom karenge.
04:41
Phir hum T, B maloom karenge.
04:43
Aur dono ko plus karke humare paas A, B aa chahega.
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