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Thread: Rectangle: Find diagonals

  1. #1
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    Rectangle: Find diagonals

    The diagonal of the rectangle is twice as long on one side. Calculate the acute angle between diagonals.
    Need a bit help with this, can someone explain it to me.
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  2. #2
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    Re: Rectangle: Find diagonals

    When you draw a diagonal of a rectangle, you separate it into two right triangles. You know know the relationship between the hypoteneuse and one of the sides of the triangle is 2:1. There is a very specific right triangle that has this relationship. Which one is it?
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    Re: Rectangle: Find diagonals

    30-60-90 triangle? But how do I do the calculations?
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    Re: Rectangle: Find diagonals

    Quote Originally Posted by Enzyme View Post
    30-60-90 triangle? But how do I do the calculations?
    You say, any right triangle with a ratio of hypotenuse to a side of 2:1 is a 30-60-90 triangle. That is the calculation. There are no more calculations.
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    Re: Rectangle: Find diagonals

    Quote Originally Posted by Enzyme View Post
    The diagonal of the rectangle is twice as long on one side. Calculate the acute angle between diagonals.
    Are you trying to calculate the angles at the center, where the diagonals cross?
    CLARIFY your darn problem...
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  6. #6
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    Re: Rectangle: Find diagonals

    Quote Originally Posted by Enzyme View Post
    The diagonal of the rectangle is twice as long on one side. Calculate the acute angle between diagonals.
    Need a bit help with this, can someone explain it to me.
    Rectangle: Find diagonals-untitled20.gif
    You are correct $\Delta ACD$ is a $30-60-90$ degree triangle.
    We know that $AC=2AD$

    But the diagonals of a rectangle are of equal length and bisect each other.
    Therefore $AD=AE$ so that $\Delta AED$ is an equilateral triangle. Can you explain why?

    Now can you find the measure of $\angle AED~?$.
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    Re: Rectangle: Find diagonals

    Refere attachment please.
    Attached Thumbnails Attached Thumbnails Rectangle: Find diagonals-capture.jpg  
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