Chapter 13, Trigonometric Ratios and Functions - 13.1 Use Trigonometry with Right Triangles - 13.1 Exercises - Problem Solving - Page 858: 37

$59$ meters

Let $h$ be the height of the building. $h=\dfrac{50}{(\cot 32^{\circ}-\cot 53^{\circ})}$ This gives: $h=\dfrac{50}{(1.6000335-0.753554)}$ $h \approx 59$ meters Hence, the height of the building is $59$ meters.