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Thread: 3D trig

  1. #1
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    3D trig

    Help me with this question please

    http://i667.photobucket.com/albums/v...0001/wedge.jpg

    Thank you in advance
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  2. #2
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    Hello anonymous_maths
    Quote Originally Posted by anonymous_maths View Post
    Help me with this question please

    http://i667.photobucket.com/albums/v...0001/wedge.jpg

    Thank you in advance
    I'm assuming that all the angles at $\displaystyle B$ and $\displaystyle C$ are right-angles.

    Then, in the diagram I've attached, $\displaystyle N$ is the required point on $\displaystyle FE$; $\displaystyle P$ is the foot of the perpendicular from $\displaystyle N$ to the base; and the required angle, $\displaystyle a = \angle NDP$.

    Then, from $\displaystyle \triangle NDP,\, \tan a = \frac{NP}{DP}= \frac{6}{DP}$

    $\displaystyle \Rightarrow DP = \frac{6}{\tan a}$

    Note now that $\displaystyle FN = CP$, and then consider $\displaystyle \triangle DPC$. By Pythagoras' Theorem: $\displaystyle CP^2 = DP^2 - DC^2$

    $\displaystyle \Rightarrow FN = CP = \sqrt{\Big(\frac{6}{\tan a}\Big)^2- 12^2}=\sqrt{\frac{36}{\tan^2a}-144}$

    Grandad
    Attached Thumbnails Attached Thumbnails 3D trig-untitled.jpg  
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