Question

3) There is a coconut tree on the bank of a river from a boat 5 m above the water, the angle of
elevation of the top of the tree is 45° and the angle of depression of reflection of tree top is
60'. Find the height of the tree.

Answer 1

3) There is a coconut tree on the bank of a river from a boat 5 m above the water

Given,

In Δ PQR

tan 45° = QR / PQ

= h-5 / x

1 = h-5 / x

x = h - 5  .........(1)

In Δ PQS

tan 60° = SQ / PQ

= h+5 / x

√3 = h+5 / x

x = (h + 5) / √3  ..........(2)

equating (1) and (2), we get,

h - 5 = (h + 5) / √3  

√3 (h - 5) = h + 5

√3h - 5√3 = h + 5

√3h - h = 5 + 5√3

h (√3 - 1) = 5 (√3 + 1)

h = 5 (√3 + 1) / (√3 - 1)

Rationalizing the above factor, we get,

h = 5 (2 + √3) m

Therefore, the height of the tree is 5(2 + √3) m