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Math Help - Trigonometry

  1. #1
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    Trigonometry

    Don’t know where to start here

    The length of a diagonal of a rectangle is 10cm. The diagonal is inclined at an angle \theta^{\circ} to a side of the rectangle. Show that the perimeter, P cm, of the rectangle is given by:

    P = 20\sqrt{2}\sin(\theta + 45)^{\circ}
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  2. #2
    MHF Contributor red_dog's Avatar
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    AC=10, \ \widehat{CAD}=\theta

    CD=10\sin\theta, \ AD=10\cos\theta

    P=20(\sin\theta+\cos\theta)=20\left(\sin\theta+\si  n\left(\frac{\pi}{2}-\theta\right)\right)=20\cdot2\sin\frac{\pi}{4}\cos  \left(\frac{\pi}{4}-\theta\right)=

    =20\sqrt{2}\sin\left(\frac{\pi}{4}+\theta\right)
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