Question

To find the width of the river, a man observes the top of a tower on
the opposite bank making an angle of elevation 61°. When he moves
50 m backward from bank and observes the same top of the tower,
his line of vision makes an angle of elevation of 35º. Find the height
of the tower and width of the river. (tan 61° = 1.8, tan 35º = 0.7)
ople of elevation of
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Answer 1

Here is your answer

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

Answer 2

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