Since there is a 90° angle and a 45° angle, the third angle is

180° - (90° + 45°) = 180° - 135° = 45°

So the triangle has two congruent acute angles and so it is
an isosceles right triangle.  That means both legs have the same
measure, and since we are given that the horizontal leg is 1500 
feet, the vertical leg, which is the tower, is also 1500 feet.
Notice that an isosceles right triangle (often called a 45-45-90
triangle) is one-half of a square cut down the diagonal, as you
can see from the drawing below:


Edwin