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Thread: Urgent! How to find inner angles and side of the rhombus given height and diagonal e?

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    Exclamation Urgent! How to find inner angles and side of the rhombus given height and diagonal e?

    We are given in rhombus that height is equal h = 2\sqrt{3} cm and diagonal AC = 4\sqrt{3} cm. Find length of a rhombus side a, other diagonal BD all inner angles.
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    Re: Urgent! How to find inner angles and side of the rhombus given height and diagona

    Ask someone to help you translate your problem to proper English.

    And do you know what a rhombus is?
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    Re: Urgent! How to find inner angles and side of the rhombus given height and diagona

    Quote Originally Posted by lebdim View Post
    We are given in rhombus that height is equal h = 2\sqrt{3} cm and diagonal AC = 4\sqrt{3} cm. Find length of a rhombus side a, other diagonal BD all inner angles.
    something like this?

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    Re: Urgent! How to find inner angles and side of the rhombus given height and diagona

    Nice picture! Calling the vertex at (0,0) "A" and going around counter clockwise, labeling vertices A, B. C, D, then a= h cos(\theta)= 2\sqrt{3}cos(\theta) where \theta is angle BAD. Further, triangle ABC is an isosceles triangle with base angles \theta/2 and two sides of length a. By the "cosine law", the length of the third side, the diagonal AC is given by |AC|^2= (4\sqrt{3})^2= 48= a^2+ a^2+ 2a^2 cos(\theta/2). That gives two equations,
    a= 2\sqrt{3}cos(\theta) and (4\sqrt{3})^2= 48= 2a^2(1+ a^2 cos(\theta/2)) to solve for a and \theta.
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    Re: Urgent! How to find inner angles and side of the rhombus given height and diagona

    The coordinates are to scale ... all right triangles are 30-60-90.
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    Re: Urgent! How to find inner angles and side of the rhombus given height and diagona

    @HallsofIvy,

    I have a question. How can be the side a = h\cos{\theta}, if a is a hypotenusis? Isn't it \sin{\theta} = \frac{h}{a}?

    And cosine-law, I got: a^{2} = a^{2} + e^{2} - 2\cdot{a}\cdot{e}\cdot\cos{\frac{\theta}{2}}? Made I mistake, where e = \left|AC\right|?
    Last edited by lebdim; Nov 6th 2016 at 01:10 AM.
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