You don't really have to use trig functions- these are "special angles. If the angle at point a is 60 degrees, the right triangle formed is half of an equilateral triangle. If the base, the distance from the tower to point a, is "x" (half of one side of the equilateral triangle) then the hypotenuse is 2x (one side of the equilateral triangle) so the height of the is, by the Pythagorean theorem, . That is 36 meters so , . That is, point a is 12\sqrt{3}= 20.7 m or, to the nearest meter, 21 m as you say.

Similarly, 45 degrees is exactly half of 90 degrees- a right triangle with one angle 45 degrees has the other acute angle 45 degrees also so is an isosceles triangle. That means that the distance from the tower to b is exactly the same as the height of the tower, 36 m. Now, on the ground, we have a right triangle with one leg the distance from the tower to a, 20.7 m, and hypotenuse of length 36 m. The width of the river is the other leg of that right triangle.