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The shadow of an 8 m tall building is of length 6 m on the ground. Which of the following is the distance of the end point of the shadow from the top of the building?
9 m
12 m
6 m
10 m
10 m
Recognize the Pythagorean triplet (3,4,5). Scaling by a factor of 2, we get (6,8,10), which directly gives the hypotenuse as 10 m.
Height of the building (h) = 8 m, length of the shadow (b) = 6 m.
c=h2+b2тАЛ
Recognize the Pythagorean triplet (3,4,5). Scaling by a factor of 2, we get (6,8,10), which directly gives the hypotenuse as 10 m.
Students often mistake this for a trigonometry problem involving angles, or attempt to calculate the area instead of the hypotenuse distance.
Identify Geometric Model
The building and its shadow form a right-angled triangle where the building height is the perpendicular (8┬аm) and the shadow is the base (6┬аm).
P=8,B=6
Apply Pythagoras Theorem
To find the distance from the top of the building to the end of the shadow (hypotenuse), we use the relation c=P2+B2тАЛ.
c=82+62тАЛ
Final Calculation
Square the values: 82=64 and 62=36. Sum them: 64+36=100. Take the square root: 100тАЛ=10.
c=64+36тАЛ=100тАЛ=10┬аm
D is correct because the hypotenuse of a right-angled triangle with legs 8┬аm and 6┬аm is 10┬аm.
This concept is fundamental for Trigonometry (Height and Distance chapters) and coordinate geometry distance formulas.
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