The length of a shadow of a building is 32 m . the distance from the top of the building to the tip of the shadow is 38 m . find the height of the building. if necessary, round your answer to the nearest tenth.

For this case the first thing you should realize is that you have a rectangle triangle where you have two of the three sides.
 Therefore, to solve the problem, you must find the third side using the
 Pythagorean theorem.
 We have then:
 h ^ 2 + 32 ^ 2 = 38 ^ 2
 We cleared h:
 h = root (38 ^ 2 - 32 ^ 2)
 h = 20.49390153
 round to the nearest tenth
 h = 20.5 m
  
 the height of the building is: 
 h = 20.5 m