Question 1210262: Let ABC be a triangle with side lengths AB = 5, BC = 6, and AC = 9. What is the area of the triangle with side lengths \tan A$, \tan B, and \tan C?
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
Let ABC be a triangle with side lengths AB = 5, BC = 6, and AC = 9.
What is the area of the triangle with side lengths tan(A), tan(B), and tan(C)?
~~~~~~~~~~~~~~~~~~~~~~~~~~
This problem's formulation looks strange, but I will interpret it " as is ",
i.e. in a way as I read it.
Compare |AB|^2 + |BC|^2 with |AC|^2.
We have 5^2 + 6^2 = 25 + 36 = 61 for |AB|^2 + |BC|^2 and 9^2 = 81 for |AC|^2.
Since |AB|^2 + |BC|^2 = 61 is less than |AC|^2 = 81, we conclude that angle B is obtuse.
If so, then tan(B) is negative.
The implication is that such a triangle with the sides tan(A), tan(B) and tan(C) does not exist.
Solved.
|
|
|
