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Math Help - Transposition of Formula

  1. #1
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    Transposition of Formula

    I want to find the height of a pole H

    From a distance, I measure the angle (Theta 1) to the top of the pole.
    I then move a distance D towards the pole and measure the angle to the top of the pole again (Theta 2). I do not know my distance from the pole so call it X

    I know that H/X=Tan(Theta 2)
    I also know that H/(X+D)=Tan(Theta 1)

    I know by transposition that H=X(tan(Theta 2)) & H=(X+D)(Tan(Theta 1))

    To find H I need to find X

    This is where I get lost in my Transposition!!

    Can anybody please help me, I'm loosing a lot of sleep over this
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  2. #2
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    Quote Originally Posted by berniecole View Post
    I want to find the height of a pole H

    From a distance, I measure the angle (Theta 1) to the top of the pole.
    I then move a distance D towards the pole and measure the angle to the top of the pole again (Theta 2). I do not know my distance from the pole so call it X

    I know that H/X=Tan(Theta 2) (1)
    I also know that H/(X+D)=Tan(Theta 1) (2)

    I know by transposition that H=X(tan(Theta 2)) & H=(X+D)(Tan(Theta 1))

    To find H I need to find X

    This is where I get lost in my Transposition!!

    Can anybody please help me, I'm loosing a lot of sleep over this
    Solve (1) for x. Plug in this term into (2) and solve for H:

    \dfrac Hx = \tan(\theta_2)~\implies~ x = \dfrac H{\tan(\theta_2)} Therefore the second equation becomes:

    H=(x+D)\tan(\theta_1)~\implies~ H=\left(\dfrac H{\tan(\theta_2)} + D\right) \tan(\theta_1)

    Solve this equation for H.
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  3. #3
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    How do I combine the 2 Hs in the final equation?

    Regards
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  4. #4
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    Quote Originally Posted by berniecole View Post
    How do I combine the 2 Hs in the final equation?

    Regards
    <br />
H=(x+D)\tan(\theta_1)~\implies~ H=\left(\dfrac H{\tan(\theta_2)} + D\right) \tan(\theta_1)<br />

    1. Expand the bracket:

    H=\dfrac {H \cdot \tan(\theta_1)}{\tan(\theta_2)} + D \cdot \tan(\theta_1)

    2. Take the term containing H from the RHS to the LHS:

    H-\dfrac {H \cdot \tan(\theta_1)}{\tan(\theta_2)} = D \cdot \tan(\theta_1)

    3. Factor out H:

    H\left(1-\dfrac {\tan(\theta_1)}{\tan(\theta_2)}\right) = D \cdot \tan(\theta_1)


    4. Divide by the bracket.
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  5. #5
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    Smile Transposition of Formula

    Many thanks for your explanation, it was greatly appreciated.

    Clearly I now need to develop my factoring skills, this is where I fell down.

    Regards

    Berniecole
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