= Solution
Interpreting the cone as \b[<Cherenkov radiation>], its angle gives the speed, not directly the <mass>:
$$
\cos\theta=\frac{c}{nv}=\frac1{n\beta},\qquad\gamma=\left(1-\frac1{n^2\cos^2\theta}\right)^{-1/2}.
$$
Combining this with the relativistic <kinetic energy> $T=(\gamma-1)mc^2$ gives the <Cherenkov mass inference>
$$
\boxed{m=\frac{T}{c^2\left[\left(1-\frac1{n^2\cos^2\theta}\right)^{-1/2}-1\right]}.}
$$
The material must be transparent at the observed <frequency>, $n$ is its <phase refractive index> there, and $n\cos\theta>1$. For $T>0$ this requires $0<\theta<\arccos(1/n)$ for a massive particle above threshold. Radiation of an unspecified other origin would not determine the <mass> from these data alone.
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