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# Help!

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An equilateral triangle has two vertices at (0,5) and (8,5). If the third vertex is in the first quadrant, what is the y-coordinate? Express your answer in simplest radical form.

Feb 17, 2019

$$\text{The point will have it's }x \text{ coordinate at the midpoint of the given points}\\ x=4\\ \text{the distance from the point to say }(0,5) \text{ is equal to the (squared) distance between the given points}\\ (4-0)^2+(y-5)^2 = 8^2\\ 16 + (y-5)^2 = 64\\ (y-5)^2 = 48\\ y = \pm \sqrt{48}+5 = \pm 4\sqrt{3}+5\\ \text{the point that lies in the first quadrant is thus }\\ (x,y) = (4, 4\sqrt{3}+5)$$