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.
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.
To determine the height of the street light, we can use similar triangles and basic trigonometry. The triangle formed by the man, his shadow, and the street light is proportional to the triangle formed by the man, his new shadow, and the height of the street light.
First, let's calculate the height of the man using the given information. We have the man's height (1.8 meters) and his initial shadow length (6.5 meters).
Using the concept of similar triangles, we can set up a proportion:
height of man / length of shadow = height of street light / length of shadow
1.8 / 6.5 = height of street light / 9.1
To find the height of the street light, we can rearrange the equation:
height of street light = (height of man / length of shadow) * length of new shadow
height of street light = (1.8 / 6.5) * 9.1
height of street light ≈ 2.52 meters
Therefore, the street light is approximately 2.52 meters tall.