Let P represent Point Ilisium, L the Lake Edge, and S the Shore Ita.
Draw triangle PLS. We are given `m/_L=59^@,m/_S=36^@,LS=28`
Using the Law of Sines we have the following extended proportion:
`(PL)/sinS=(PS)/sinL=(LS)/sinP` . Substituting the known values we get:
`(PL)/sin36^@=(PS)/sin59^@=28/sinP` . The measure of angle P is 180-(59+36)=85.
The area of the triangle is given by `"Area"=1/2 a b sinC` where C is the angle included between sides a and b.
So the area of triangle PLS is `"Area"=1/2(16.52)(28)sin59^@~~198.26`
So the distance from P to L is approxiamtely 16.52km, the distance from P to S is approximately 24.09km, and the area of the triangle is approximately 198.26 square km.