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Math Help - 4 problems

  1. #1
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    4 problems



    Write an expression for tan x degrees and an expression for tan(90-x)degrees, in terms of a, b, and c. How is the tangent of an angle related to the tangent of the angle's complement?



    Write and expression for (sin X degrees)squared + (cos x degrees) squared in terms of a, b, and c. Then use the Pythagorean Theorem to simplify your expression





    A) Use triangel ACD to write expressions for p squared + q squared in terms of b and for p in terms of b and angle A.

    B) Find a squared in terms of c, p and q. Give your answer in expanded form.

    C) Use results from parts a and b to find an expression for a squared in terms of b, c and angle A

    D) Use the results from part c to find the angle A round your final answer to the nearest tenth. (with this problem is triangle ABC with side lengths AB = 27 AC=32 BC= 23)


    other problem:
    when the sun is shining at a 62 degree angle of depression, a flagpole forms a shadow of length x feet. Later the sun shines at an angle of 40 degrees, and the shadow is 25 feet longer than before

    a) Draw a picture of the scenario

    B) write two expressions for the height of the flagpole in terms of x

    C) how tall is the flagpole to the nearest tenth of a foot


    Thanks a please show all work.
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  2. #2
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    Quote Originally Posted by abc123 View Post
    ...

    other problem:
    when the sun is shining at a 62 degree angle of depression, a flagpole forms a shadow of length x feet. Later the sun shines at an angle of 40 degrees, and the shadow is 25 feet longer than before

    a) Draw a picture of the scenario

    B) write two expressions for the height of the flagpole in terms of x

    C) how tall is the flagpole to the nearest tenth of a foot


    Thanks a please show all work. How about showing what you have done so far?
    to a) see attachment

    to b) Use the tan-function:

    \tan(62^\circ)=\dfrac hx ..... \tan(40^\circ)=\dfrac h{x+25}

    to c) Solve the first equation for x: x=\dfrac h{\tan(62^\circ)}
    and plug in the term of x into the second equation:

    \tan(40^\circ)=\dfrac h{\dfrac h{\tan(62^\circ)}+25}

    Solve for h. (For your confirmation only x \approx 37.88)
    Attached Thumbnails Attached Thumbnails 4 problems-flagmast_schatten.png  
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