SOLUTION: A 6ft. tall person standing at a distance of 27ft. from the water tower must look up at an angle of 46degrees to see the top of the water tower. To the nearest foot, find the heigh

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Question 188583: A 6ft. tall person standing at a distance of 27ft. from the water tower must look up at an angle of 46degrees to see the top of the water tower. To the nearest foot, find the height of the water tower?
Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!


Let's see the man standing away from the Water Tower.
drawing%28400%2C400%2C-1.5%2C10%2C-1%2C12%2Ccircle%280%2C3%2C.25%29%2Cline%280%2C2.75%2C0%2C.5%29%2Cline%280%2C.5%2C-.5%2C0%29%2Cline%280%2C.5%2C.5%2C0%29%2Cline%280%2C1.5%2C-.15%2C1.5%29%2Cline%280%2C1.5%2C.15%2C1.5%29%2Cline%288%2C0%2C8%2C11%29%2Cline%288%2C11%2C8.4%2C11%29%2Cline%288.4%2C11%2C8.4%2C0%29%2Cline%288.4%2C0%2C8%2C0%29%2Cgreen%28line%280%2C3%2C8%2C3%29%29%2Cgreen%28arrow%280%2C3%2C8%2C11%29%29%2Cred%28locate%281.75%2C4.5%2Csigma=46%5Eo%29%29%2Cline%280%2C0%2C8%2C0%29%2Cgreen%28locate%283%2C.5%2CDistance=27ft%29%29%2Cgreen%28arrow%28-1%2C0%2C-1%2C3%29%29%2Cred%28locate%28-.8%2C2.5%2C6ft%29%29%2Cgreen%28locate%287.8%2C8%2CWater%29%29%2Cgreen%28locate%287.8%2C7.6%2CTower%29%29%2Cred%28locate%288.7%2C8.5%2CX%29%29%2Cred%28locate%288.7%2C2%2CY=6ft%29%29%29
We can see by Trigonometric Function, we can get X
tan%28sigma%29=opp%2Fadj
tan%2846%5Eo%29=X%2F27ft
X=%2827%29tan46%5Eo}---> X=27.9ft

*Remember, Height of Water Tower = X + Y =27.9ft + 6ft=33.9ft or 34ft, Answer

Thank you,
Jojo