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A vertical stick 11 m long casts a shadow 7 m long on the ground. At the same time, a tower casts a shadow of 35 m long on the ground. The height of the tower is:
52 m
55 m
50 m
60 m
55 m
Observe the ratio of the tower's shadow to the stick's shadow: 35/7 = 5. Therefore, the tower height is simply 5 times the stick height: 11 ├Ч 5 = 55 m.
Vertical stick height (h1) = 11 m, shadow length (s1) = 7 m. Tower shadow length (s2) = 35 m.
s1тАЛh1тАЛтАЛ=s2тАЛh2тАЛтАЛ
Observe the ratio of the tower's shadow to the stick's shadow: 35/7 = 5. Therefore, the tower height is simply 5 times the stick height: 11 ├Ч 5 = 55 m.
Students often invert the ratio or confuse the height with the shadow length. Always maintain the proportion (Height/Shadow) = Constant.
Establish Proportion
Since the angle of elevation of the sun is the same for both objects at the same time, the ratio of height to shadow is constant.
ShadowstickтАЛHeightstickтАЛтАЛ=ShadowtowerтАЛHeighttowerтАЛтАЛ
Substitute Values
Plug in the known values: height of stick = 11, shadow of stick = 7, shadow of tower = 35.
711тАЛ=35HтАЛ
Solve for H
Cross-multiply to solve for the height of the tower (H).
H=711├Ч35тАЛ=11├Ч5=55┬аm
B is correct because the proportionality constant calculation gives 11 ├Ч 5 = 55 m.
This concept of similar triangles is foundational for Height and Distance problems in trigonometry, often tested in CAT and SSC exams.
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