Let the height of the tower be h, and let the complementary angles of elevation from 9 m and 16 m be alpha and 90 degrees minus alpha respectively. Using the tangent function, we have tan alpha equals h divided by 9, and tan of 90 degrees minus alpha equals h divided by 16. Because tan of 90 degrees minus alpha is cot alpha, we get cot alpha equals h divided by 16. Multiplying the two equations gives tan alpha multiplied by cot alpha equals 1, which equals h squared divided by 144, meaning h squared is 144. Taking the positive square root gives the height of the tower as 12 m.