How can I prove that the angles of the tetrahedral structure is $109.5^\circ$ with calculus. I could do it with geometry.
120285
Angle between lines joining tetrahedron center to vertices
118501
Proving the length of a circle's arc is proportional to the size of the angle
15135
Find angle UFO in the picture attached
18005
Angle notation for complex numbers in polar form
86753
All right angles are equal to each other
48586
Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
75679
How to prove that $2 \arctan\sqrt{x} = \arcsin \frac{x-1}{x+1} + \frac{\pi}{2}$
22767
How to prove $3^\pi>\pi^3$ using algebra or geometry?
119417
Tetrahedron inequality
95473
Complex Numbers Geometry
1859
Proving $\arctan(\sqrt{x^2+1}-x)=\frac{\pi}{4}-\frac{1}{2}\arctan(x)$
46621
Relationship between the side lengths of a tetrahedron and an inscribed tetrahedron with vertices at the centroids
45584
In $\triangle ABC$ with $AB=AC$ and $\angle BAC=20^\circ$, $D$ is on $AC$, with $BC=AD$. Find $\angle DBC$. Where's my error?
90708
Comparing angles and working out the difference
47342
Figure out if a fourth point resides within an angle created by three other points
138236
What is the sum of the angles of a triangle on Earth orbit?
124425
A geometry question: Let $ABCD$ be a convex quadrilateral. Prove that AD is parallel to BC.