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Math Help - world problem please help! Trigonometric Ratios and Special Angles

  1. #1
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    world problem please help! Trigonometric Ratios and Special Angles

    So this is basically the question

    matt is flying his kite at the end of a 40 meters string. The string makes and angle of pi/4 with the ground. The wind speed increases, kite flies higher until the string makes an angle of pi/3 with the ground.

    Question:

    Determine an exact expression for the horizontal distance that the kite moves between the two positions.


    So far I got this

    X2=40
    ---
    √2
    X1=20

    Now im just subtracting these two and I got this

    40-20√2
    -----------=the diference but my books answer is 20 (√2-1)
    √2
    I would like to know how the book got that answer, I think my answer just needs to be simplfy but I cant get the same answer. When i calulate both i get the same answer. Please help!! this is really bothering me!!!
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  2. #2
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    Quote Originally Posted by jepal View Post
    So this is basically the question

    matt is flying his kite at the end of a 40 meters string. The string makes and angle of pi/4 with the ground. The wind speed increases, kite flies higher until the string makes an angle of pi/3 with the ground.

    Question:

    Determine an exact expression for the horizontal distance that the kite moves between the two positions.
    40 meters, angle of 45 degrees ... horizontal distance = 40/√2 = 20√2

    same 40 meters , angle of 60 degrees ... new horizontal distance = 20
    (short leg is half the hypotenuse, right?)

    20√2 - 20 = 20(√2 - 1)
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  3. #3
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    Quote Originally Posted by skeeter View Post
    40 meters, angle of 45 degrees ... horizontal distance = 40/√2 = 20√2

    same 40 meters , angle of 60 degrees ... new horizontal distance = 20
    (short leg is half the hypotenuse, right?)

    20√2 - 20 = 20(√2 - 1)
    Thank you for the reply. I still dont understand how is this possible

    40/√2 = 20√2. Please explain or can you point me to a website where they explain this. I really struggle with these radical stuff!! thank u again!
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  4. #4
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    Quote Originally Posted by jepal View Post
    Thank you for the reply. I still dont understand how is this possible

    40/√2 = 20√2. Please explain or can you point me to a website where they explain this. I really struggle with these radical stuff!! thank u again!
    this method is called rationalizing the denominator ...

    \frac{40}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{40 \sqrt{2}}{2} = 20 \sqrt{2}
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  5. #5
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    ok just to clarify when rationalizing the denomintor, do u multiply both numerator and denominator with the radical. Thank u so much
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  6. #6
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    Quote Originally Posted by jepal View Post
    ok just to clarify when rationalizing the denomintor, do u multiply both numerator and denominator with the radical. Thank u so much
    both ... you're really multiplying by 1
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