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Math Help - Height of a mt

  1. #1
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    Height of a mt

    In traveling across flat land you notice a mountain directly in front of you. Its angle of elevation is 3.5 degrees. After you drive 13 miles closer to the mountain the angle of elevation is 9 degrees. Approx. the height of the mountain.

    Is this problem able to be solved with out the law of sines? I can solve this problem if I use the law of sines and get the Hypotenuse, then use Cos(9)=y/hypot.


    Thank you
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  2. #2
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    let h = height of mountain

    x = horizontal distance from final stop to a point directly beneath the mountain top

    \displaystyle \tan(3.5^\circ) = \frac{h}{x+13}<br />

    \displaystyle \tan(9^\circ) = \frac{h}{x}


    solve the system for h
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  3. #3
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    But that leaves me two variables still. So I will multiply both sides by x to get .1583844403x=h. When I do the law of sines I get 8.280294046 for the height.
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  4. #4
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    Do I solve both for h and set each equal to one another again to find x then plug into equations to solve. Just been a while since had to do that. Law of sines easier. Thank you
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