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Calculating Angle in a Pyramid

Alexander Ross • • 2 min read
Calculating Angle in a Pyramid
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I have the question "Calculate the angle between the length AE and the base ABCD in the pyramid pictured below, giving your answer to 1 decimal place."

For this question I know we have to find the angle A. Firstly what I done is I dissected the pyramid through the middle from E so that I can form a right angled triangle.

I then used Pythagoras to find the length of side AE and the line though the middle.

I then used the Sine rule to try and find the angle A in which I got 81.7 degrees, however the solutions say that the answer should be 77.8 degrees.

Here is my working:

Where have I gone wrong ?

Edit:

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1 Answer

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The angle you actually want is $\angle EAC$, so you need $$\cos^{-1}\frac{3}{10\sqrt{2}}=77.8^o$$

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Alexander Ross
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Alexander Ross

Alexander Ross has covered the video game industry for a decade, writing deep dives on game design, esports tournaments, VR developments, and gaming culture.