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Understanding Height and Distance: Practical Applications of Trigonometry

This resource delves into the principles of height and distance measurement using trigonometry, specifically focusing on angles such as 30°, 45°, and 60°. It includes step-by-step explanations and examples that illustrate how to calculate heights based on known distances and angles. By understanding these concepts, students can apply their knowledge to real-world situations, making it a valuable learning tool for mathematics and geometry courses. Equipped with practical examples, this guide enhances clarity and comprehension.

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Understanding Height and Distance: Practical Applications of Trigonometry

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  1. Height and Distance rxbIrisMG.gurjIqisMG.jsivMdrisMG jmwq=dsvI srkwrI.sInIAr.sYkMfrI.skUl.auksIsYxIAW.ijlwpitAwlw

  2. BUimkw • iqkoximqI iv`c AsI iek smkox iqRBuj dI vrqo krdy hW [ • ies leI AsI iemwrq mInwr , phwV jW dr`Kq Awid nU iek lMbwqmk ryKw dy rUp ivc Aqy AwdmI jW phwVI dI cotI Awid nUM iek ibMdU dy rUp ivc drswaudw hY [

  3. idRStIryKw • jdo AsI iksy vsqU nMU dyKdy hW qW swfI A`K Aqy aus vsqU nUM imlwaux vwlI ryKw idRStI nUM AsI ryKw AwKdy hW [

  4. aucwxkox jykr koeI vsqU swfI A`K dI lytvI ryKw qo au`pr qW swNnMU vsqU nUM dyKx leI isr nUM au`pr cu`kxw pvygw [ies qrw swfIAw A`KW iek kOx nwl a`pr v`l GuMm jwdIAw hn [ ies kox nUM AsI aucwx kOx AwKdy hW [

  5. invwx kox • jykr koeI vsqU swfI A`Kw dI lytvI ryKw qo hyTW hovy qW swnMU vsqU nMU dyKx leI isr nMU hyTw krnw pvygw ies qrw swfIAw A`Kw ie`k kox nwl hyTw v`l GuMm jWdIAW hn ies kox nUM AsI invwx kox AwKdy hW [

  6. audwrhx • iek mInwr DrqI a`pr is`Dw KVw hY [mInwr dy ADwr qO 30 mItr dUrI qy siQq i`k ibMdU qO mInwr dI cotI dw aucwx kxo 60 hY [ mInwr dI aucweI pqw kro [ • h`l : • mMn lau AB mInwr hY Aqy C mInwr dy ADwr ibMdU 30 mI : dUr DrqI qy siQq auh ibMdU hY , ijs qo mInwr dI cotI dw aucwx kox 60 hY [mInwr ryKw KMf dy rUp ivc drswaudy hoey AsI pRSn nUM icqr 13 .5 ivc idKwey Anuswr drsw skdy hW [

  7. hux tan 60=AB/BC (ies leI tanø =lMb/ADwr) • =>tan60 =AB/30 [ies leI bc =30 mI: ] • => anderehood 3×30 =ab [ies leI tan 60=3] • Bwv AB =30 anderehood 3 miter: • Anderehood 3×1.732lYx qy • AB =[30×1.732] mI.= 51.96 mI.

  8. audwrhx • nUMryKwKMfdyrUpiv`cdrswkyAsIpRSnnMUic`qr 13.7 iv`cidKweyAnuswrdrswskdyhW [ huxsmkoxIiqkox ABC< ivc sin 45= ab /ac [¿ iesleI sin ø =lMb /krx • jW 1/ anderehood 2 =12/ac ikauik ac 12 anderehood 2 • =12×1.414 • =16.968 • iesqrwqwrKMbydyADwribMdU (Bwv B ) qo 16.97 mI : dIdUrIqyjmInivcd`bIhY [ • iekibjlIdyKMbydIaucweI 12 mI : hY [ DrqIqyisDKVwr`KxleIiesdyisryqyiekstIldIqwrbMnIhY [ ijsdwdUsrwisrwbxwaudIhovyqWd`SoikqwrKMbydyADwribdUqOikMnIdUrqyjmInivcjmInivcdibAwhoieAwhY [jykriehstIldIqwrDrqI 45dwkOxd`bIhoeIhY ? • h`l :mMnlau AB ibjlIdwKMbwhYAqy ACÇ stIldUIqwrhY [ ibjlIdyKMby

  9. audwrhx • DrqIa`pris`DyKVyi`ek 10 mI ; a`ucyKMbydya`prlyisryqyie`kr`swbMinAWhYijsdwdUsrwisrwDrqIau`qysiQqkIqwigAwhY [ie`kklwkwrDrqIqor`syrwhIKMbydyaprlyisryv`ljwirhwhYjykrDrqInwl 30dwkoxbxwaudwhovyqWd`soikklwkwrnMUkMbydyisryq`kphMcxleIiknIdUrIqihkrnIpvygI [ • h`l : • mMnlau AB ie`k 10 mI: au`cwKMbwhYAqy AC r`swhYijsdw • isrwDrqIqysiQqhY [ klwkwribMdU C isryqoisryv`ljwrhIhY [ KMbynMUryKwKMfAqyAwdmInMUibMdUrUpivcdrswauxnwlAsIpRSnnMUic`qr 13.8 ivc` idKweyAnuswrdrswskdyhW [ • huxsmkoxIiqRkox ABC ivc

  10. sin 30 AB/AC [ ies leI sin ø =lMb /krx • Bwv =1/2 =10/ AC • jW AC =10×2 =20 • ies qrW klwkwr nMU KMby dy isry q`k phuMcx leI 20 mI : dUrI qYA krnI pvygI [

  11. DMnvwd

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