Tetrahedron

What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?

Correct result:

A =  54.736 °

Solution:

a=1 h1=a2(a/2)2=12(1/2)20.866 x=23 h1=23 0.8660.5774 cos(A)=x/a A=180πarccos(x/a)=180πarccos(0.5774/1)=54.736=54448"a=1 \ \\ h_{1}=\sqrt{ a^2-(a/2)^2 }=\sqrt{ 1^2-(1/2)^2 } \doteq 0.866 \ \\ x=\dfrac{ 2 }{ 3 } \cdot \ h_{1}=\dfrac{ 2 }{ 3 } \cdot \ 0.866 \doteq 0.5774 \ \\ \cos (A)=x/a \ \\ A=\dfrac{ 180^\circ }{ \pi } \cdot \arccos(x/a)=\dfrac{ 180^\circ }{ \pi } \cdot \arccos(0.5774/1)=54.736 ^\circ =54^\circ 44'8"



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