Integer tangents?
Geometry
Level
4
We know the tangents of the angles of a triangle are positive integers.
Compute:
The answer is 6.
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1 solution
From property of triangles, we know that
t a n ( α ) + t a n ( β ) + t a n ( γ ) = t a n ( α ) t a n ( β ) t a n ( γ )
Let t a n ( α ) = n 1 , t a n ( β ) = n 2 , and t a n ( γ ) = n 3 , where n 1 , n 2 & n 3 are positive integers.
Therefore, n 1 + n 2 + n 3 = n 1 n 2 n 3 , which has only one solution ( 1 , 2 , 3 ) . Hence, t a n ( α ) + t a n ( β ) + t a n ( γ ) = 6 .