Trigonometric problem solving culminates in this chapter. Leave no side and no angle unmeasured!

**NOTE:** This length can be expressed as \(\sqrt{\dfrac{A}{B}}\), where \(A,B\) are coprime positive integers. Submit the value of \(A+B\) as your answer.

Aeroplanes A and B are flying with constant speed in the same vertical plane at angles 30° and 60° with respect to the horizontal, respectively, as shown in the figure.

The airspeed of A is \(100 \sqrt{3} \) meters per second. Initially, an observer in A sees B directly ahead and at the same altitude at a (horizontal) distance of 500 m.

Assuming they take no evasive action and collide, after how many seconds does this happen?

Give your answer to 3 decimal places.

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