The base of a pyramid is a right triangle with

Dominick Blanchard 2022-05-07 Answered
The base of a pyramid is a right triangle with the longest side = 12cm. All non base edges are also equal to 12cm. And how can I find the height of the pyramid?
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Answers (1)

Corinne Choi
Answered 2022-05-08 Author has 15 answers
Use Thales' theorem.
You can select the points
A = ( 6 , 0 , 0 ) , B = ( + 6 , 0 , 0 ) ,
to form the longest side of the base triangle. The other point C lies on a circle of which A B is the diameter, as
y 2 + [ 6 x ] 2 + y 2 + [ 6 + x ] 2 = 144 ,
so
x 2 + y 2 = 36
The top point T is given by ( 0 , 0 , z ) and it is clear that
| A T | = | B T | = | C T |
as A, B and C lie on the same circle, as | A T | = | B T | = | A B |, we obtain
z = 6 3
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