Q6 of 31 Page 122

When the sun is at an elevation of 35°, the shadow of a tree is 10 metres. What would be the length of the shadow, when the sun is at an elevation of 25°?

Let the height of the tree be x metre.



In right Δ BAC,


AC = x and AB = AD + DB = (10 + y) m


AC = tan 25° × AB


⇒ x = tan 25° × (10 + y)


(From table, tan 25° = 0.466)


⇒ x = 0.466 × (10 + y) …(i)


In right Δ DAC,


AC = x and AD = y


AC = tan 35° × AD


⇒ x = tan 35° × (y)


(From table, tan 35° = 0.7)


⇒ x = 0.7 × y …(ii)


Dividing eq. (i) from eq. (ii),



⇒ 0.7(y) = 0.466(10) + 0.466(y)


⇒ 0.7(y) – 0.466(y) = 0.466(10)


⇒ 0.234 (y) = 4.66


⇒ y = 19.91 m


AB = 10 + y = 10 + 19.91 = 29.91 m


Length of shadow at 25° = AB = 29.91 m


Length of shadow = 29.91 m


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