NTSE Stage 2 SAT 2017 Question Paper

Question : 60 of 100

Marks: +1, -0

ABC is a field in the form of an equilateral triangle. Two vertical poles of heights 45m and 20m are erected at A and B respectively. The angles of elevation of the tops of the two poles from C are complementary to each other. There is a point D on AB such that from it, the angles of elevation of the tops of the two poles are equal. Then AD is equal to-

$17 5/12 \m$
$20 10/13 \m$
$20 5/13 \m$
$17 10/12 \m$

Validate

Solution:

\tan(90-\θ)=\cot \θ

20/\BC=\AC/45\;\;\;\;\;\;\;\(\let \AC=\BC=\x)

\x^2=900\;\;\;\;\;\;\;\;\x=30

Let

\AD=9\y,\BD=4\y

∴

9\y+4\y=30

\;\;\;\;\;\;\y=30/13

∴

\AD={9×30}/13

\;\;\;\;\;\;\;\;\=270/13

\AD=20(10/13)\m

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