A man ina boat rowing away from light house 200m high takes 2 minutda to change the angle of elevation of the top of the lighthouse from 60degree to 45degree find the speed of the boat
Answers
Given:-Height of lighthouse=200m
Time taken to reach angle of elevation 60° to 45° = 2 min.
Let , the distance of boat from lighthouse at 60°= AB cm
and , the distance of boat from lighthouse at 45° = CB cm
Firstly , the distance b/w the boat and the lighthouse at the angle of 45°=
tan 45° = 200 m / CB
1 = 200 m / CB
CB = 200 m ............... equation 1
Now , the distance b/w the boat and the lighthouse at the angle of 60° =
tan 60 = 200 m / AB
√3 = 200 m / AB
AB√3 = 200 m
AB = 200 m / √3 ............ equation 2
For the distance b/w boats at different cases , subtract eq. 2 from eq. 1=
CB - AB =200 - 200√3
= 200√3 - 200÷ √3
= 146/ √3
=146 / 1.73
= 84.39 m
As we know that speed = distance / time
so,
speed of the boat = 84.39/2 min.
= 42.195 m/min. ( answer)
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Answer:
84.39/2 min
Explanation:
Speed of the boat = 84.39/2 min
= 42.195m /min