Question

A flag pole 4 m tall casts a 6 m., shadow. At the same time, a nearby building casts a shadow of 24 m. How tall is the building ?
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Answer 1

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Answer 2

Answer:

Given, a flag pole 4m tall with shadow 6m

And a building shadow 24m

Need to calculate the building

In Δ ABC and Δ PQR

⇒ ∠ B = ∠ Q = 90°

⇒ ∠ C = ∠ R

At any instance all sun rays are parallel, AC || PR

⇒ by AAA similarity we have in two triangles if the angles are equal, then sides opposite to the equal angles are in the same ratio (or proportional) and hence the triangles are similar.

⇒ Δ ABC ∼ Δ PQR

⇒ By Converse proportionality theorem we have

if a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.

⇒  $\frac{AB}{PQ}$=$\frac{BC}{QR}$

⇒  4/x=6/24

⇒ PQ =  24*4/6

= 16m