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The angle of elevation theta of a light house as seen by a person on the ground is such that tan theta = 5/12. Whwn the person moves a distance of 240m towards the light house,the angle of elevation becomes x such that tan x = 3/4. Find the height of the light house. 

Asked by chittukala7 7th December 2015, 6:31 PM
Answered by Expert
Answer:

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.

L e t space A B space b e space t h e space h e i g h t space o f space t h e space l i g h t space h o u s e. L e t space C space b e space t h e space p o i n t space o f space o b s e r v a t i o n space a n d space B C equals y L e t space theta space b e space t h e space a n g l e space o f space e l e v a t i o n. C o n s i d e r space t h e space r i g h t space t r i a n g l e space A B C. T h u s comma space tan theta equals fraction numerator A B over denominator B C end fraction rightwards double arrow 5 over 12 equals fraction numerator A B over denominator y end fraction rightwards double arrow y equals fraction numerator 12 A B over denominator 5 end fraction... left parenthesis 1 right parenthesis A l s o space g i v e n space t h a t comma space w h e n space t h e space o b s e r v e r space m o v e s space a space d i s tan c e space o f space 240 space m space t o w a r d s space t h e space l i g h t space h o u s e comma t h e space a n g l e space o f space e l e v a t i o n space i s space x space s u c h space t h a t space tan x equals 3 over 4 therefore tan x equals fraction numerator A B over denominator B D end fraction comma space w h e r e space D space i s space 240 space m space d i s tan t space f r o m space C. rightwards double arrow 3 over 4 equals fraction numerator A B over denominator y minus 240 end fraction rightwards double arrow y minus 240 equals fraction numerator 4 A B over denominator 3 end fraction rightwards double arrow y equals 240 plus fraction numerator 4 A B over denominator 3 end fraction... left parenthesis 2 right parenthesis E q u a t i n g space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma fraction numerator 12 A B over denominator 5 end fraction equals 240 plus fraction numerator 4 A B over denominator 3 end fraction S o l v i n g space t h e space a b o v e space w e space h a v e comma A B equals 225 space m H e i g h t space o f space t h e space t o w e r space i s space 225 space m.

Answered by Expert 7th December 2015, 6:47 PM
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