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Math Help - 'Real word' Trig Question

  1. #1
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    'Real word' Trig Question

    ONE
    The angle of depression from the top of a 25-m high building to the top of the building across the street is 5 degrees and to the floor of the building is 47 degrees. What is the heigh of the other building and how wide is the tstreet.

    State answers to the nearest meter

    TWO
    A flag pole is tied to the ground by two steel cables. One cable is 27 metres long and the other is 19 meters. The cables are attached to the ground at points A and B that are 5 meters from each other. The points A and B and the foot of the flagpole are in a straight line. What is the height of the flagpole, if the cables attached to it 1.5 below its top. STate your answers to the nearest tenth of a meter.


    I LITERALLY have no idea how to do these.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by prettiestfriend View Post
    ONE
    The angle of depression from the top of a 25-m high building to the top of the building across the street is 5 degrees and to the floor of the building is 47 degrees. What is the heigh of the other building and how wide is the tstreet.

    State answers to the nearest meter

    .
    First of all , draw a diagram and you will get 2 triangles .

    Let the width of the street be y .

    tan 47 =25/y . You can find the width .

    tan 5= h /y(the answer above)

    Final height = 25-h
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  3. #3
    Super Member
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    Quote Originally Posted by prettiestfriend View Post

    ...

    TWO
    A flag pole is tied to the ground by two steel cables. One cable is 27 metres long and the other is 19 meters. The cables are attached to the ground at points A and B that are 5 meters from each other. The points A and B and the foot of the flagpole are in a straight line. What is the height of the flagpole, if the cables attached to it 1.5 below its top. STate your answers to the nearest tenth of a meter.

    I LITERALLY have no idea how to do these.
    As mathaddict stated:
    First of all , draw a diagram and you will get 2 triangles.


    Label the distance from the shorter cable where it attached to the ground (at point B) to the base of the flag pole as 'b'

    Label the distance from the base of the flag pole to the longer cable where it is attached to the ground (at Point A) as 'b+5'


    Label the distance from the base of the flag pole to the POINT WHERE THE CABLES ARE ATTACHED near the top of the flag pole as 'h'


    You should recognize (from your sketch) that you have two right triangles.


    Equation1
     27^2 = h^2 + (b+5)^2
    &
    Equation2
     19^2 = h^2 + b^2

    subtracting

     27^2 - 19^2 = (b+5)^2 - b^2

    expanding the () part

     27^2 - 19^2 = b^2 + 10b + 5^2 - b^2
    some simplification
     27^2 - 19^2 = 10b + 25
    &more
     27^2 - 19^2 - 25 = 10b
    & dividing
     \frac{27^2 - 19^2 - 25}{10} = b

    Plug that back into Equation2 to get the dimension 'h' and then ADD the 1.5 metres to the top of the flag pole.

     h = \sqrt{19^2 - b^2 }

    & finally the HEIGHT of the flagpole is  h + 1.5
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