Rain Rain come back another day

When a man moves down the inclined plain with constant speed 5 \(\text{ms}^{-1}\) which makes an angle of \(37^{\circ}\) with the horizontal, he finds that the rain is falling vertically downward. When he moves up the same inclined plane with the same speed, he finds that the rain makes an angle \(\theta\) = \(\arctan{\left( \frac{7}{8} \right)}\) with the horizontal. The speed of the rain (w.r.t man) can be expressed as \(a\sqrt{b}\).

Give your answer as \(a^2 + b^2\)

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