SSC BOARD PAPERS IMPORTANT TOPICS COVERED FOR BOARD EXAM 2024

### A tree is broken by the wind. The top struck the ground at an angle of 30º and at a distance of 30 m from the root. Find the whole height of the tree. ( √3 = 1.73)

5. A tree is broken by the wind. The top struck the ground at an angle of 30º and at a distance of 30 m from the root. Find the whole height of the tree. ( √3 = 1.73)

Sol. seg AB represents the height of the tree

The tree breaks at point D

∴ seg AD is the broken part of tree which then takes the position of DC
m∠ DCB = 30º
BC = 30 m
In right angled ∆DBC,
tan 30º = side opposite to angle 30º/adjacent side of 30º
∴ tan 30º = BD/BC
∴ 1/√3 = BD/30
∴ BD = 30/√3
∴ BD = (30/√3)×(√3/√3)
∴ BD = 10√3 m
cos 300 = adjacent side of angle 300/Hypotenuse

∴ cos 300 = BC/DC
∴ cos 300 = 30/DC
∴ √3/2  = 30/DC
∴ DC = (30×2)/√3
∴ DC = (60/√3)×(√3/√3)
∴ DC = 20√3 m
AD = DC = 20 √3 m
AB = AD + DB [∵ A - D - B]
∴  AB = 20 3 + 10 3
∴  AB = 30 3 m
∴  AB = 30 × 1.73
∴  AB = 51.9 m

The height of tree is 51.9 m.