an aeroplane at an altitude of 250m observes the angle of depression of two boats on opposite banks of a river to be 45 degree and 60 degree respectively find width of river(please include diagram and explaination to each step)

Asked by ushanihar12 | 4th Feb, 2019, 09:14: PM

Expert Answer:

L e t space A space b e space t h e space p o s i t i o n space o f space a n space a e r o p l a n e comma space B space a n d space C space b e space t h e space t w o space b o a t s space o b s e r v e d space f r o m space t h e space a e r o p l a n e
D space i s space t h e space p o i n t space o n space B C space w h i c h space m a k e s space a n space a l t i t u d e space w i t h space A
T h e space t w o space b o a t s space B space a n d space C space o n space o p p o s i t e space b a n k s space o f space a space r i v e r space m a k e s space a n g l e space o f space d e p r e s s i o n space 45 to the power of o space end exponent a n d space 60 to the power of o space r e s p e c t i v e l y.
I n space triangle A B D comma space
tan space 45 to the power of o equals fraction numerator A D over denominator B D end fraction equals 250 over x comma space w h e r e space B D equals x
rightwards double arrow x equals fraction numerator 250 over denominator tan space 45 to the power of o end fraction space equals 250 space m space equals space B D

N o w space i n space triangle A D C comma
tan space 60 to the power of o equals fraction numerator A D over denominator D C end fraction equals 250 over y comma space w h e r e space D C equals y
rightwards double arrow y equals fraction numerator 250 over denominator tan space 60 to the power of o end fraction space equals fraction numerator 250 over denominator square root of 3 end fraction equals fraction numerator square root of 3 space cross times space 250 over denominator 3 end fraction space equals 144.3 space m space equals space D C
W i d t h space o f space t h e space r i v e r space equals space B C space equals space B D space plus D C
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis 250 plus 144.3 right parenthesis space m
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 394.3 space m

Answered by Renu Varma | 5th Feb, 2019, 11:59: AM