A vertical pillar of length 40 m on a bridge is supported by a slanting iron rod. One end of the rod is fastened to the tip of the pillar and the other end to the bridge at a distance of 30 m from the pillar. What is the length of the iron rod? Draw a diagram to represent this.
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Height of pole=AB=6 m
Length of shadow of pole =BC=4 m
Length of shadow of tower=EF=28 m
In △ABC and △DEF
∠B=∠E=90∘ both 90∘ as both are vertical to ground
∠C=∠F (same elevation in both the cases as both shadows are cast at the same time)
∴△ABC∼△DEF by AA similarity criterion
We know that if two triangles are similar, ratio of their sides are in proportion
So,DEAB=EFBC
⇒DE6=284
⇒DE=6×7=42 m
Hence the height of the tower is 42 m
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