how tall was the flagpole

Question

 A flagpole is bent over by the wind so the top is now touching the ground 18feet from the base , the angle the pole makes with the ground is 75 degree.  How tall was the pole before the wind storm

Answer 1

I am assuming that the flagpole is bent in a circle segment curve and that the 75 degrees angle is formed by the tangent to the circle at the contact point with the soil. so we will have an isosceles triangle formed by the cord which is the soil with a length equal to 18 ft. Being this said, then the triangle formed by the two radius and the cord has two angles of 15 degrees and one of 150 degrees. By the Sin theorem, we have that

(18/sin150)=(r/sin 15) solving for r we obtain r= 9.32 ft. the total circumference will be 2*pi*r = 58.56 ft.

The arc formed by the flagpole will be the one enclosed in the 150 degrees angle. so: (58.56/360)*150 = 24.4 feet. that was the height of the flagpole when was vertical.

I made a lot of assumptions but there is no other way of solving the problem.