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An electric pole casts a shadow of length 42 m at a time when a tree 12 m high casts a shadow of length 16 m. Find the height of the pole.
31.5 m
30.5 m
29 m
33 m
31.5 m
The height of the electric pole is found using the principle of similar triangles, as the sun's rays make equal angles with the ground at the same time of day. By setting up a direct proportion between the heights and shadows of the pole and the tree, we can solve for the unknown height.
The height of the electric pole is found using the principle of similar triangles, as the sun's rays make equal angles with the ground at the same time of day. By setting up a direct proportion between the heights and shadows of the pole and the tree, we can solve for the unknown height.
If you stand next to a tall building at noon, your shadow and the building's shadow are stretched at the exact same angle. That means if the building is 3 times taller than you, its shadow will also be 3 times longer than yours.
Height over Shadow is always constant, like a photo stretched in proportion.
S1тАЛH1тАЛтАЛ=S2тАЛH2тАЛтАЛ тАФ Ratio of height to shadow length for similar triangles
H2тАЛ=S2тАЛ├Ч(S1тАЛH1тАЛтАЛ) тАФ Formula to calculate unknown height
At any given instant, the angle of elevation of the sun is the same for all vertical objects standing on horizontal ground. This forms similar right-angled triangles where the ratio of the height of an object to the length of its shadow remains constant: Shadow1тАЛHeight1тАЛтАЛ=Shadow2тАЛHeight2тАЛтАЛ.
Shadow lengths are directly proportional to object heights when measured simultaneously.
The sun's rays can be considered parallel due to the immense distance of the sun from Earth.
Units of height and shadow must be consistent (both in meters).
Allows indirect measurement of very tall objects without physical scaling.
Requires simultaneous measurement under identical lighting conditions.
Determining heights of trees, towers, and minarets using shadow geometry.
Astronomical distance estimations using parallax and proportional geometry.
Calculation: h=1612├Ч42тАЛ=16504тАЛ=31.5┬аm
Option A is correct because substituting the given values into the proportion equation yields exactly 31.5 m.
A is correct тАФ The height of the electric pole calculated via similar triangles is 31.5 m.
Always ensure that the ratio terms (Height/Shadow) maintain the same numerator and denominator convention to avoid inversion errors.
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