I need to find the coordinate for the third point

Question

The side of the Bermuda triangle are all roughly 1000 miles long. From miami at (0,0), San Juan at (10,0). Find Bermudas coordinates?

Answer 1

This is an equilateral triangle. If the base is along the x-axis at points (0,0) and (10,0), it has a side length of 10 - 0 = 10 units.

Draw the equilateral triangle. By symmetry, the third point will be hanging above the middle of the base at x = 10/2 = 5.

Split the triangle into two right triangles by dropping the height from the third point towards the base.

Take the left right triangle - it has a base of 10/2 = 5 units along the x-axis, an angle of 60 degrees at the base, and a height y.

Using trigonometry for the right triangle: tan60° = y/5

Therefore, y = 5tan60°

The coordinates of the third point are (x, y) = (5, 5tan60°).