Calculate some things about a tetrahedron

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SUMMARY

The discussion centers on calculating geometric properties of a tetrahedron with equilateral triangle faces, specifically focusing on the lengths and angles related to its surfaces. The tetrahedron has sides measuring 2 units. The user successfully calculated the perpendicular length from vertex A to the plane BCD and the angle between surfaces ACD and BCD, but encountered discrepancies in calculating the angle between edge AB and plane BCD. The correct angle is confirmed to be 53.1 degrees, while the user's calculation yielded approximately 54 degrees, indicating a potential rounding error in their method.

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Question Statement:
Each surface of a tetrahedron ABCD is an equilateral triangle with each side 2 units long. The midpoint of AB and CD are L and M respectively. Calculate, by giving your answers correct to 3 s.f. or to the nearest 0.1 degree,

a) The length of the perpendicular from A to the plane BCD
b) The angle between the surface ACD and BCD
c) Angle between AB and the plane BCD

My Attempt So Far :
I have solved part A and B. The only part that confuse me is part C.
My calculation :
let the angle between AB and the plane BCD be x.
The perpendicular distance from A to the plane BCD be p.
So sin x = p/AB = 1.63/2

But the answer given is x = 53.1 degree, which is slightly smaller than the answer I found.

Is the method I used wrong?
 
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Just looking quickly the answer you have may be less due to rounding error. How much less is your answer than the answer given in the book?
 
1 degree. The answer given is 53.1 degree, wheres mine is about 54 degrees.
 

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