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anonymous

  • 5 years ago

The angle of elevation to the top of the radio atenna on the top of a building is 53.4 degrees. After moving 200 feet closer to the building, the angle of elevation is 63.4 degrees. Find the height of the building if the height of the atenna is 189 feet. Please HELP!

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  1. amistre64
    • 5 years ago
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  2. amistre64
    • 5 years ago
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    is the height of the antennea AT 189 ft? or is the antennea 189FT tall?

  3. anonymous
    • 5 years ago
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    imaging right triangle, where is the h (hight of the building) is one side of the triangle + 189 ft for antenna now if alpha= angle 53.4 and beta= angles 63.4 on a bottom (other side of the right triangle) - length x will become (x-200) after it's moved so, tan alpha = (h+189)/x tan beta=(h+189)/(x-200) you know angles; you have a system of two ew with two variables - should be able to solve it. let me know if there is a problem

  4. anonymous
    • 5 years ago
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    Actually the height of the antenna is 180ft. Sorry, my mistake!

  5. anonymous
    • 5 years ago
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    just input 180 instead of 189 in the above. should work the same

  6. amistre64
    • 5 years ago
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    ..... antennea = 180? ...... or top of antennea is at 180' ?

  7. anonymous
    • 5 years ago
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    Oh and the antenna is 180ft tall.

  8. amistre64
    • 5 years ago
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    the antennea is bigger than a football field at the moment

  9. anonymous
    • 5 years ago
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    Haha.

  10. amistre64
    • 5 years ago
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    tan(53.4) = (180+h)/(200+d) tan(63.4) = (180+h)/(d)

  11. amistre64
    • 5 years ago
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    d = (180+h)/tan(63.4) tan(53.4) = (180+h)/(200+[(180+h)/tan(63.4)]) tan(53.4.) = (180+h)/[(tan(63.4)180 + 180 + h)/tan(63.4)]

  12. amistre64
    • 5 years ago
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    lets clean this up with a = tan(53.4) and b=tan(63.4) a = (180+h)/[(200b + 180 + h)/b] 180b + hb a = --------------- 200b + 180 + h

  13. amistre64
    • 5 years ago
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    ... see if iniks way works better lol

  14. amistre64
    • 5 years ago
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    1.3465 = (180+h)/(200+[(180+h)/1.9969) 1.3465 = (180+h)/[(579.392+h)/1.9969]) 2.69 ---------- = 180 + h 579.392 +h 2.69 = (180 +h) (579.392 +h) 2.69 = h^2 +759.392h +104290.56 ...... this is messy :)

  15. anonymous
    • 5 years ago
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    Thank you SO much!

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