SOLUTION: The segment connecting point A(1,2) to point B(4,2) is one side of a 30�-60�-90� triangle, , but you do not know which side. It could be the shorter leg, the longer leg or the hyp

Question 722346: The segment connecting point A(1,2) to point B(4,2) is one side of a 30�-60�-90� triangle, , but you do not know which side. It could be the shorter leg, the longer leg or the hypotenuse.
How many 30�-60�-90� triangles can be drawn under these conditions?
For each triangle, state:
� the coordinates of point C.
� the lengths of the 3 sides.
I have all the lengths of all sides of every triangle and the coordinate C for every triangle except four.
I have all 12 possible triangles, but when AB is the hypotenuse, I cannot find the coordinate of C.
Please help me find a way or a formula to solve for coordinate C when I have all side lengths and two other points? Thank you very much!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The length from A to B is 3
---
If AB is the hypoteuse, the side opposite the 30 degree
angle is (1/2)(3 = 3/2
------------------------------
The side opposite the 60 degree angle is [sqrt(3)/2]*3 = (3/2)sqrt(3)
====================================================
Cheers,
Stan H.
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