The situation in the problem creates a right triangle with a base of 14ft. An angle of 65 degrees means that the triangles has...
A hypotenuse of [tex]hyp = \frac{14ft}{cos(45)} = 33.13ft[/tex], representing the length of the broken part of the pole.
An opposite of [tex]sin(65)*hyp = sin(65)*33.1ft = 30.0ft[/tex], representing the height of the part of the flag that still stands.
The total original flag height is the sum of the two parts.
[tex]h = 30.0ft + 33.13ft = 63.13ft[/tex]
