The diagonals of a rhombus are 3.5 and 12, a circle tangents two sides (or their extensions) of the rhombus and the center is on the one of the vertices of the rhombus. Find the exact value of the circle area. (Make a drawing for all cases)

"curse these trig-loving pirates! " devora mutters as she looks at the map. then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 48 meters along the way. after performing a calculation, devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 89 meters to the treasure. supposing that the angle at the cave entrance is acute and that devora's calculations were correct, how many degrees did she turn?