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Math Help - Trig word problem help

  1. #1
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    Trig word problem help

    The shadow of a city building is observed to be 100 m long. At the same time the shadow of a lamp post 9 m high is observed to be 5.5 m long. Find the altitude of the sun, and the height of the building.

    -----
    I'm thinking that since there are no angles given, the proportionality theorem of triangles will be applied. But I have doubts. So, how do you solve this?
    Thanks.
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  2. #2
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    Quote Originally Posted by fayeorwhatsoever View Post
    The shadow of a city building is observed to be 100 m long. At the same time the shadow of a lamp post 9 m high is observed to be 5.5 m long. Find the altitude of the sun, and the height of the building.

    -----
    I'm thinking that since there are no angles given, the proportionality theorem of triangles will be applied. But I have doubts. So, how do you solve this?
    Thanks.
    1. Draw a sketch. (see attachment)

    2. Use proportions:

    \dfrac h9 = \dfrac{100}{5.5}~\implies~h \approx 163.36\ m

    3. Use the Tangens function to calculate the altitude of the sun (presumeably you mean the angle of elevation above the horizon?)

    \tan(\phi)=\dfrac9{5.5}~\implies~\phi \approx 58.57^\circ
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