Heights and Distances Practice Test 2

Question : 24 of 24

Marks: +1, -0

From the top of a h metre high cliff the angles of depression of the top and the bottom of a tower are observed to be 30° and 60° respectively. The height of the tower is:

$h √3$
$2 h √3$
$h/3$
${2h}/3$

Validate

Solution:

Let AB = h m be the height of cliff and CD = x m be the height of the tower and also ∠ ADB = 60° and ∠ ACE = 30°.
Now, from the figure, AE = (h – x)m
From right triangle ABD, BD = h cot 60° =

h/√3

m
From right triangle CEA, (h – x) = EC tan 30° = BD tan 30°

⇒h-x=h/√3 . 1/√3

⇒h={2h}/3m

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