Question
Tue March 17, 2015 By: Akansha Parihar

as observed from the top of the lighthouse, 100m high above sea level , the angle of depression of a ship changes from 30 degrees to 60 degrees.
determine the distance travelled by ship during the period of observation.

Expert Reply
Vimala Ramamurthy
Wed March 18, 2015
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.
H e r e space h e i g h t space o f space t h e space t o w e r comma space A B equals 100 m L e t space B C equals x space a n d space C D equals y C o n s i d e r space t h e space triangle A B C tan 60 degree equals fraction numerator A B over denominator B C end fraction equals 100 over x rightwards double arrow square root of 3 equals 100 over x rightwards double arrow x equals fraction numerator 100 over denominator square root of 3 end fraction space m C o n s i d e r space t h e space triangle A B D tan 30 degree equals fraction numerator A B over denominator B D end fraction equals 100 over y rightwards double arrow fraction numerator 1 over denominator square root of 3 end fraction equals 100 over y rightwards double arrow y equals 100 square root of 3 space m W e space k n o w space t h a t comma B D equals B C plus C D rightwards double arrow y equals x plus C D rightwards double arrow C D equals y minus x rightwards double arrow C D equals 100 square root of 3 minus fraction numerator 100 over denominator square root of 3 end fraction equals fraction numerator 100 cross times open parentheses 3 minus 1 close parentheses over denominator square root of 3 end fraction equals fraction numerator 100 cross times 2 over denominator square root of 3 end fraction equals fraction numerator 200 over denominator square root of 3 end fraction space m T h u s space t h e space d i s tan c e space t r a v e l l l d space b y space t h e space s h i p space d u r i n g space t h e space p e r i o d space o f space o b s e r v a t i o n space i s space fraction numerator 200 over denominator square root of 3 end fraction space m
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