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  4. The x- axis, y- axis and a line passing through the point A (6, 0) form a triangle ABC. If angle A=30° , then the area of the triangle, in sq.units is

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Q. The $ x- $ axis, $ y- $ axis and a line passing through the point A (6, 0) form a triangle $ABC$. If $ \angle A=30{}^\circ , $ then the area of the triangle, in sq.units is

KEAMKEAM 2007Straight Lines

Solution:

In $ \Delta AOB,tan\,30{}^\circ =\frac{OB}{OA} $

$ \Rightarrow $ $ \frac{1}{\sqrt{3}}=\frac{OB}{6} $
$ \Rightarrow $ $ OB=\frac{6\sqrt{3}}{3}=2\sqrt{3} $
$ \therefore $ Area of $ \Delta AOB=\frac{1}{2}\times OA\times OB $
$=\frac{1}{2}\times 6\times 2\sqrt{3}=6\sqrt{3} $ sq unit

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