A person 1.65 meters tall casts 1.8 m shadow At the same instance,a lamp post casts a shadow of 5.4 m find the height of the lamp post
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Answered by
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See the diagram.
The angle subtended by the Sun rays when they meet the ground is the same at one point of time in the day. So the Sun rays hitting the top of the head of the person and the top of the lamp post make the same angle with the ground (or the horizon).
The triangles APP' and BLL' are similar triangles (two angles are same in the two triangles). So the ratios of sides are same.
PP' / AP = BB' / BP
BB' = height of the lamp post = PP' * BP / AP
= 1.65 m * 5.4 m / 1.8 m
= 4.95 m
The angle subtended by the Sun rays when they meet the ground is the same at one point of time in the day. So the Sun rays hitting the top of the head of the person and the top of the lamp post make the same angle with the ground (or the horizon).
The triangles APP' and BLL' are similar triangles (two angles are same in the two triangles). So the ratios of sides are same.
PP' / AP = BB' / BP
BB' = height of the lamp post = PP' * BP / AP
= 1.65 m * 5.4 m / 1.8 m
= 4.95 m
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The Sun rays are all parallel in one region, as Sun is very very far away from Earth. This is the reason for All Sun rays to make the same angle with the horizon or ground.
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