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Math Help - Triangle trig prob.

  1. #1
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    Triangle trig prob.

    The Leaning Tower of Provlle creates an 85 degree angle between itself and the level ground around the tower. The tower's shadow is 100 feet long. If it can be determined, which of the following expressions gives the distance, in feet, from the top of the tower to the ground?

    Turns out it can't be determined but is this because 100 cot 85 = x and so x = 8ft and an 8ft building can't cast a 100ft shadow or is there some other reason??
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    Super Member angel.white's Avatar
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    Quote Originally Posted by donnagirl View Post
    The Leaning Tower of Provlle creates an 85 degree angle between itself and the level ground around the tower. The tower's shadow is 100 feet long. If it can be determined, which of the following expressions gives the distance, in feet, from the top of the tower to the ground?

    Turns out it can't be determined but is this because 100 cot 85 = x and so x = 8ft and an 8ft building can't cast a 100ft shadow or is there some other reason??
    I would expect it is because the length of the shadow will change with the position of the sun, unless you know the angle that the sun makes to something in relation to the tower, you will not know how long the shadow should be. For instance, if the sun is near the horizon, it will cast a long shadow, so the tower may be short in order to make a 100foot shadow. But if the sun is almost directly overhead, the tower may need to be very tall to cast a 100 foot shadow.

    Another thought is that you would need to know not only the angle of elevation of the sun, but also which direction the tower is leaning, for instance if it is leaning at 85 degrees, and the sun is at 85 degrees, and the tower is pointing towards the sun, it won't make a shadow at all. But if it is pointing away from the sun, it will make a shadow, and if the shadow is 100 feet, then the tower would be 573.7 feet.

    So it would seem that you would need to know the exact position of the sun in the sky with respect to the orientation of the tower on the ground.
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