Question

A man standing at the edge of a river sees the top of a tree at an elevation of 60° . Stepping 20 metres back he sees it at an elevation of 30° . Draw a rough figure and find the width of the river?​

Answer 1

Answer:

(i) Let height of the tree be H meter.

In rt ∠d △ACD, tan 60˚ = H/CD

√3 = H/CD

∴ CD = H/√3 …(i)

In rt ∠d △ABD

tan 30 = H/BD

1/√3 = H/BD

∴ BD = √3H …(ii)

BD – CD = 50

√3H/1 – H/√3 = 50 [Using (i) and (ii)]

∴ (3H – H)/√3 = 50

∴ 2H = 50√3

Or H = 50√3/2 = 25√3

H = 43.3 m

(i) The width of the river CD = 25√3/√3 = 25 m

(ii) The height of the tree H = 43.3 m

Step-by-step explanation:

Hope it helps (~‾▿‾)~