Heights and Distances Practice Test 2

Question : 23 of 24

Marks: +1, -0

The angles of elevation of the top of a tower h m tall, from two different points on the same horizontal line are x and y(x > y). What is the distance between the points?

$h(\tan x - \tan y)$
$h/{\tan x\tan y}$
${h(\tan x-\tan y)}/{\tan x\tan y}$
${h(\tan x \tan y)}/{\tan x-\tan y}$
None of these

Validate

Solution:

In ΔABC,

\tan x={AB}/{BC}=h/a

⇒ a = h \cot x

......(i)
and in ΔABD,

\tan y={AB}/{BD}=h/{a+b}

⇒a+b=h\cot y

⇒b=h(\cot y-\cot x)

[using Eq. (i)]

={h(\tan x \tan y)}/{\tan x-\tan y}

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