At a certain time of the day, a man, 6 feet tall, casts his shadow 8 feet long. Find the length of the shadow cast by a building 45 feet high, at the same time. [3 Marks]

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Solution

[1 Mark]

Let the length of the shadow of the building be x.
As the source of light is the sun, XZ ∥ PQ and, hence ∆YXZ ∼ ∆YPQ.

Therefore,  $\frac{H e i g h t o f t h e M a n}{H e i g h t o f t h e B u i l d i n g}$ =  $\frac{L e n g t h o f S h a d o w C a s t b y t h e M a n}{L e n g t h o f S h a d o w C a s t b y t h e B u i l d i n g}$ [1 Mark]

⟹  $\frac{6 f t}{45 f t}$ =  $\frac{8 f t}{x}$

⟹ x = 60 feet. [1 Mark]

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