# Related Rates

**Calculus**Level pending

Two lines intersect at \( O \) making an angle of \( 2 \theta \) between them, where \( \theta =30^{\circ} \). \( T \) is a point on their angle bisector that is \( a = 5 \) units away from \( O \). Point \( A \) is on one line and point \( B \) is on the other line such that \( A \) , \( T \) and \( B \) are collinear.

If point \( A \) is moving with constant speed of 1 unit per second towards point \( O \). How fast is point \( B \) moving away from point \( O \), at the instant when \( x = | OA | = 5 \)?

Give your answer to 3 decimal places.

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