Trigonometry
In this question Trigonometric ratios are used
Transcript
00:00This is unit 6, Signometry and Bearing, exercise 6.5.
00:04Two men on opposite sides of a tree in line with it, they observe that angles of elevation
00:09of top of tree are 30 degrees and 60 degrees.
00:14The height of our tree is 15 meters, we have to find the distance between them.
00:18Simple question hai, sabse pehle aapke paas ek straight line aa jayegi, that is 15 meters.
00:24Ye height ho gayi tree ki.
00:26Ab aapke paas do log hai.
00:28Dono tree ke opposite directions peh kadein, jo door khada hai, let's suppose yaha pe
00:34ek person khada hai, to uska angle of elevation chota hoga.
00:38Angle of elevation ye hota hai ki agar aap neeche khade ho aur aap upar ki taraf dekh
00:43rahe ho.
00:44Doosra person jo ke iske kareeb khada hai tarakht ke, uska angle of elevation zyada
00:49hoga.
00:50Humme malum karna hai ki ye jo do log hain, inke darmayan kitna faasla hai.
00:55Aap is point ko T name kar do aur isko C kar do.
00:59Ab aapke paas do triangles hai.
01:03A, C, T, B, C, T.
01:07Aap dono ko solve karoge.
01:13Ab aap dekho ki aap is pe kya lagaoge, 10 through proper brush.
01:19So, 10, 30 degrees, perpendicular aur base aapke paas kya jayega 80.
01:3310 kya hota hai aapke paas, ki aapka perpendicular aur base aata hai.
01:39Through proper brush aapka perpendicular aajayega aur aapka base aajayega.
01:43To base aapke paas 80 hai.
01:45To 30 ki value kar hum calculator se calculate karein, to humme milta hai 0.57 into 7, 15, 80.
01:57Ab aap kya karoge, aap cross multiplication kar sakte ho.
02:01Aap iske neeche 1 laga do.
02:03Simply iske saath multiply aajayega aur 15, 1 ke saath multiply aajayega.
02:07Jis bhi cheez ko humne malum karna hota hai, hum usko isolate karte hai.
02:17To 80 humare paas ho jayega, 15 divided by 0.577.
02:23So, final value jo aapke paas 80 ki aayegi, that is going to be 25.99 meters.
02:31Abhi humne kya kiya hai, humne chhute wale triangle ko solve kiya hai.
02:3510 humne lagaya hai yaha pe.
02:37This is perpendicular aur 80 humare paas base hai.
02:4010, 30 ki degree ki value aapne paas 0.577 hai.
02:44Cross multiplication karein.
02:4680 ko aapne malum karna hai.
02:48Jisko hum malum karte hain, usko isolate karte hain, uski value nikaal rahte hain.
02:52Ab hum aachenge bhi doosar triangle ke liye, that is in triangle BCT.
03:00Isme bhi aapka 10 lagega.
03:04Tan theta kya hota hai aapke paas?
03:06Perpendicular over base.
03:08Perpendicular humesha humari straight line hogi.
03:12Yaha pe aapke paas tan ka jo angle use ho raha hai, that is 60 degrees.
03:17Perpendicular aapke paas 15 meters hai.
03:22Aur base aap B, T likhto, T, B likhto, dono tara se same baat hai.
03:27Tan 60 degrees ki value aapke paas aa chahiye ki, square root 3.
03:35Ye table aap chaho to yaad bhi kar sakto.
03:37Yaha simple calculator se, jab aap tan 60 ki value nikaal hoge, that will be square root 3.
03:43Hum cross multiplication karenege.
03:47Square root 3 multiply ho chahega T, B ke saath.
03:50Aur 15, 1 ke saath multiply hoge, 15 hi aayega.
03:54T, B aapke paas barabar ho chahega.
03:5715 divided by square root 3.
04:02That is going to be equal 8.66 meters.
04:07Ab finally aap kya karoge?
04:09Aapke paas A, T aa gaya, that is 25.99 meters.
04:15Aapke paas T, B aa gaya, that is 8.66 meters.
04:20In dono ko plus karlo, to aapke paas A, B aa chahega.
04:23Jo ki hum is question mein maloom karna tha.
04:26That is, A, B is equal to 34.65 meters.
04:34Aani ki aapke paas jo faasla hai, wo basically 34.65 meter ka hai.
04:39Hum A, T maloom karenge.
04:41Phir hum T, B maloom karenge.
04:43Aur dono ko plus karke humare paas A, B aa chahega.