C(6,6sqrt(3)) or C(6,- 6sqrt(3)). See solution for proof.
Practice makes perfect
Let's first draw AB.
In an equilateral triangle the height from any of the vertices will bisect the opposite side. Therefore, the height of the unknown vertex must be positioned somewhere along x=6.
Additionally, all equilateral triangles have three congruent angles of 60^(∘). We have two possible triangles that can be drawn, one below the x-axis and one above.
We already know that the third vertex has an x-coordinate of 6. To find the point's y-coordinate, we have to determine the triangle's height, y. Because we know the adjacent leg to the 60^(∘) angle, we can find the opposite leg by using the tangent ratio. However, we can also use the Pythagorean Theorem.
