Agirl stands 160 cm tall she stands 360 cm away from a lamp post at night her shadow from the light is 90 cm long how high is the lam post

1. You should draw a diagram with the information given in the problem. As you can see in the figure attached, there are two triangles, so, you can calculate the height of the lamp post as below:
 
 h1/b1=h2/b2
 
 h1 is the height asked.
 b1=360 cm+ 90 cm
 b1=450 cm
 h2=160 cm
 b2=90 cm
 
 2. When you substitute these values into  h1/b1=h2/b2, you obtain:
 
 h1/450 cm=160 cm/90 cm
 
 3. Now, you must clear the height "h1". Then, you have:
 
 h1=(160 cm)(450 cm)/90 cm
 h1=72000 cm²/90 cm
 h1=800 cm
 
 How high is the lamp post?
 
 The answer is: 800 cm