SOLUTION: OABC is a tetrahedron whose faces are identical equilateral triangles of sides 8 cm each .Find its slant height. Leaving your answer correct to 3 significant figures

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Question 1074875: OABC is a tetrahedron whose faces are identical equilateral triangles of sides 8 cm each .Find its slant height. Leaving your answer correct to 3 significant figures
Answer by KMST(5328) About Me  (Show Source):
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The slant height is the height of the equilateral triangles of sides 8 cm each, that are the sides of that pyramid.
(Of course, the base is also an equilateral triangles of sides 8 cm each).
The height can be calculated using the Pythagorean theorem,
or using trigonometry.
For any equilateral triangle,
the height is sqrt%283%29%2F2=about+0.866 times the length of the side.
for that triangle, the Pythagorean theorem says
4%5E2%2Bh%5E2=8%5E2 , so 16%2Bh%5E2=64 --> h%5E2=64-16 --->. h%5E2=48 --> h=sqrt%2848%29 --> h=approximatelyhighlight%286.93%29 (correct to 3 significant figures ).