Q1 of 31 Page 122

When the sun is at an elevation of 40°, the length of the shadow of a tree is 18 metres. What is the height of the tree.


Given :
Angle of elevation = 40° and Length of shadow = 18 m.
Let the required triangle be Δ ABC.
∴ Angle of elevation = ∠ ABC = 40° and Length of shadow = AB = 18 m and Height of tree be AC.


In right Δ BAC,
AC = AB × tan 40°
⇒ AC = 18 × tan 40° (From table, tan 40° = 0.839)


⇒ AC = 18 × 0.839 = 15.102 m = 15.1 m


Height of tree is 15.1 metre.


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