SSC CGL Tier II 12 Apr 2015 Paper

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Question : 47 of 100

Marks: +1, -0

In a right angled triangle ΔPQR, PR is the hypotenuse of length 20 cm, ∠PRQ = 30°, the area of the triangle is

$50 √3 \cm^2$
$100 √3 \cm^2$
$25 √3 \cm^2$
$100/ √3 \cm^2$

Solution:

(1)

sin 30° =

{ {PQ}}/{\ {PR}}

⇒{1}/{2}= { {PQ}}/{20}

⇒{PQ}=20 ×{1}/{2}=10 {cm}

cos 30° =

{QR}/{PR}

⇒{√{3}}/{2}= { {OR}}/{20}

⇒{QR}= {√{3}}/{2}× 20=10√{3} {cm}

∴ Area of triangle PQR

= {1}/{2} ×10 × 10√{3}

=50 √{3}

square cm.

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