Draw the triangle.
If both base angles are #70˚#, and the sum of all the angles in a triangle is #180˚#, we can determine that the other angles measure is #x˚#, where #70+70+x=180#, so #x=40#.
If we have a #40˚-70˚-70˚# triangle, we can draw in its height from the top point to the midpoint of the base, creating two congruent right triangles within the isosceles triangle. In doing so, the #40˚# angle at the top of the triangle is bisected, splitting it into two #20˚# angles on either side of the triangle's altitude.
So, we now have two right triangles. Their hypotenuses are the legs of the isosceles triangle with length #12#, and we want to determine the length of the side opposite the #20˚# angle.
We should know that the #"cosine"# of an angle in a right triangle is equal to the adjacent leg, which is #1/2# the base of the isosceles triangle, divided by the hypotenuse, which has length #12#.
Therefore, we know that #cos70˚=x/12#, where #x# is #1/2# the base of the sail.
Through algebraic manipulation, we know that #x=12cos70˚=4.10#.
Since this is only #1/2# the base, the base's entire length is #8.21#".
(Note that the #4.10# value was rounded down, but when multiplied by #2# had to be rounded up.)
