Ok, the first thing to note is that the ground and the two parts of the tree form a right triangle (see image).
Side a is the (still standing) lower part of the tree, side c is the (broken off) upper part of the tree, and side b is the ground.
Since we know that the total height of the tree was 60 ft, we can write:
We now have two unknown variables, but only equation. So we need one more equation. Luckily for a right triangle we have equations that relate angles and side lenghts. The sine of an angle in the triangle equals the opposing side divided by the hypotenuse side:
By combining the two equations you can now find a and c.
Afterwards you use Pythagoras' theorem to find the one remaining unknown side b: