Q. 54.0( 4 Votes )

The shadow of a 5-m-long stick is 2 m long. At the same time, the length of the shadow of a 12.5-m-high tree is
A. 3 m

B. 3.5 m

C. 4.5 m

D. 5 m

Answer :

All we need to find is the angle of elevation of the sun. In the figure, AB is 5m long stick and BC is 2m long shadow of the stick. We join A and C to get a right-angled triangle ∆ABC. Angle of elevation of the sun is ACB.


Untitled31.jpg


In ∆ABC,



or,



Untitled32.jpg


In this figure, PQ is the tree and QS is its shadow. PSQ is the angle of elevation of the sun. So, PSQ = ACB. Join P and S. We get a right-angled triangle ∆PQS. Given, PQ = 12.5m. We use trigonometric ratio tan taking PQ as the height and QS as the base.


In ∆PQS,



or,



or,



So, the correct option is (D).

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