Woman at Sea Beach
A woman at sea beach looks up at a pole, and makes an angle of elevation of 45°, with the top of the pole. She walks 5 meters away from the pole towards the water and lay down on the sand with her back resting on the ground, face towards the sky and head towards the pole. She kept on looking at an object directly above her head. After 3 minutes she rotates her eyes by 60° to see the top of the pole. What is the approx height of the pole if the height of the woman is 2 meters. (Ignore the distance between her eyes and top of her head as well as ignore the height of her head while she is lying on the sand. Take √3 as 1.7)
2.28 m
4.28 m
42 cm
None of the above.
Cannot be determined.
Answer :4.28 m
Solution (Fast Approach)
Let us take the height of the pole as (X+2). We have added 2 as it is the height of the woman.
Now as she looks at the top of the pole, her eyes make an angle of 45° with the top of the pole.
Using the formula Tan45° = Height/ base
1 = X /Base, hence Base= X
Now she moves 5 meters away from the pole and lies down with her head towards the pole and eyes looking at the sky. This means we should not add her height in the total distance from the base of the pole.
Final distance from the pole = X + 5
As she turns her eyes by 60°, she makes an angle of elevation of 90° - 60° = 30° with the top of the pole
Tan 30° = (X + 2)/(X+5)
Solving the equation we get X = 2.28 (Tan 30°=1/√3)
Total height of the pole= X + 2 = 2.28 + 2 = 4.28 meters
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