Heights and Distances Practice Test 2

Question : 18 of 24

Marks: +1, -0

The angle of elevation from the bank of a river of the top of a tree standing on the opposite bank is 60°. The angle of elevation becomes 30° when observed from a point 40 meters backwards in a direction perpendicular to the length of the river. What is the width of the river?

10 m
20 m
30 m
40 m
None of these

Validate

Solution:

Let AB = h m be the height of the tree and BC = x m be the width of the river.

In ΔABC,

\tan60°={AB}/{BC}

⇒√3=h/x⇒h=√3x

......(i)
and In ΔABD,

\tan60°={AB}/{BD}

⇒1/√3=h/{40+x}⇒40+x=h√3

......(ii)
From (i) and (ii)

h=√3x

40+x=h√3

40+x=(√3x)(√3)

x=20x

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