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We can solve this problem using the concept of similar triangles.
Let's draw a diagram to help us visualize the situation:
A (top of pole and light source)
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| h (height of pole and light source)
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M (top of man)
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F (foot of man)
We know that the total height of the pole and the light source is 4.2 m, so we can write:
h + 180 = 420 (in cm)
Solving for h, we get:
h = 240 cm
Now, let's focus on the triangle formed by the top of the man (M), the foot of the man (F), and the light source (A). We want to find the shortest distance between the top of the man and the source of light, which is represented by the line segment MA.
We can use the fact that the two triangles formed by MAF and MAA' (where A' is the point directly below M on the ground) are similar. This means that the ratios of their corresponding sides are equal:
MA / h = AA' / h + 180
We know that h = 240 cm and AA' = 420 cm - 320 cm = 100 cm, so we can substitute these values and solve for MA:
MA / 240 = 100 / 420
MA = (240 * 100) / 420
MA = 57.14 cm
Therefore, the shortest distance between the top of the man and the source of light is approximately 57.14 cm.
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