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Math Help - What is the height of the hill?

  1. #1
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    What is the height of the hill?

    From a point on level ground, an observer measures the angle of elevation to the top of a hill to be 38 degrees The observer then walks 370 meters directly away from the hill and measures the angle of elevation to the top of the hill to be 25 degrees. Determine the height of the hill to the nearest meter.

    I drew it out and for variables I used "x" as the distance from the first angle measurement to the base of the hill and 370 from the end of the first measurement to the start of the second measurement. I used "h" to represent height. I got cot 38 degrees=x/h and cot 25=(370+x)/h I solved for x in the first equation then plugged it into the second and got finally h=370/(cot 25 - cot 35) why is this answer wrong? Thanks for the help!
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    Quote Originally Posted by dcowboys107 View Post
    From a point on level ground, an observer measures the angle of elevation to the top of a hill to be 38 degrees The observer then walks 370 meters directly away from the hill and measures the angle of elevation to the top of the hill to be 25 degrees. Determine the height of the hill to the nearest meter.

    I drew it out and for variables I used "x" as the distance from the first angle measurement to the base of the hill and 370 from the end of the first measurement to the start of the second measurement. I used "h" to represent height. I got cot 38 degrees=x/h and cot 25=(370+x)/h I solved for x in the first equation then plugged it into the second and got finally h=370/(cot 25 - cot 35) why is this answer wrong? Thanks for the help!
    because it should be 38 instead of 35 ?
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