Question

have an equilateral triangle with side length d. Two points given, A=(0,0) and B=(d,0).

find point C of the triangle.

Answer 1

You know the middle point because it is between the other two, you also know the length of the base and the hypothenuse. Use that to discover the height.

Answer 2

pythagorean theorem: (d/2)² + h² = d² (the hypothenuse)
h² = d² - (d/2)²

height \[h=\sqrt{d² - (\frac{ d }{ 2 })^{2}}\]

Answer 3

And simply that (it comes out ... I want to say nice but I don't think you will think the same). Then you point is the middle over and the height up.

Answer 4

\[h = \sqrt{d^{2}-\frac{ d^{2} }{ 4 }} = \sqrt{\frac{ 4d^{2} }{ 4 }-\frac{ 1d^{2} }{ 4 }}\]
when taking power of fraction, take power on numerator and denominator?

Answer 5

After simplifying that to \[\sqrt{\frac{ 3d ^{2} }{ 4 }}\]

you can take the square root of the top and the bottom individually.

Answer 6

\[h=\frac{ \sqrt{d^{2}3} }{ \sqrt{4} } = \frac{d\sqrt{3}}{2}\]and so
\[C=(\frac{ d }{ 2 },\frac{d\sqrt{3}}{2})\]