Question 1143510: Three posts are set in level ground in such a manner that their bases form an equilateral triangle with sides 10m long. If the heights of the posts are 6m,9m,and 15m, find the area of the triangle formed by their tops.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Three posts are set in level ground in such a manner that their bases form an equilateral triangle with sides 10m long. If the heights of the posts are 6m,9m,and 15m, find the area of the triangle formed by their tops.
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Label the tops A, B & C for the 6, 9 & 15m posts respectively.
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Find the 3 sides, AB, BC and AC
 = ~10.44
Find the other 2 sides, the same way.
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Then use Heron's Law to find the approximate area.
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A different method:
The points in 3-space are:
A(0,0,6)
B(5,5sqrt(3),9)
C(0,10,15)
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Find the cross product of AB and AC.
The area is 1/2 of that.
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