a man 1.8 metres, standing under a street light, notices that his shadow is 6.5metres. He walks 12 metres in the direction of 150 degree true bearing and he realises that his shadow is 9.1 metres. How tall is the street light.

Answer 1

I assume that by "true bearing" you mean directly away from the light. Otherwise, the direction provides no useful information.

Draw the diagram. It will include two sets of similar triangles, each with the light pole as one side. You can see that if the man started x meters from the pole, then

h/(x+6.5) = 1.8/6.5
h/(x+12+9.1) = 1.8/9.1
Solve these to get both the height and the man's initial distance.