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Math Help - Help with this trig word problem!

  1. #1
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    Help with this trig word problem!

    Two wires stretch from the top T of a vertical pole to points B and C on the ground, where C is 10 m closer to the base of the pole, than is B. If wire BT makes an angle of 35 degrees with the horizontal and wire CT makes an angle of 50 degrees with the horizontal, how high is the pole?

    I know the answer is about 16.98 meters. Please help if you know
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  2. #2
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    Quote Originally Posted by orkdork View Post
    Two wires stretch from the top T of a vertical pole to points B and C on the ground, where C is 10 m closer to the base of the pole, than is B. If wire BT makes an angle of 35 degrees with the horizontal and wire CT makes an angle of 50 degrees with the horizontal, how high is the pole?

    I know the answer is about 16.98 meters. Please help if you know
    Use tangent.

    If the distance from the base of the pole to C is x,
    then the distance to B is x+10...

    h=pole height.

    tan(50^o)=\frac{h}{x}\ \Rightarrow\ h=xtan50^o

    tan(35^0)=\frac{h}{x+10}\ \Rightarrow\ h=(x+10)tan35^o

    That's two equations for h which must be equal..

    xtan50=xtan35+10tan35

    xtan50-xtan35=10tan35

    Now factor the LHS and finish.
    Once you have x, you can find h.
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