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We report an accurate distance of d = 10+/-2.5kpc to the high-velocity cloud Complex C. Using high signal-to-noise Keck/HIRES spectra of two horizontal-branch stars, we have detected CaII K absorption lines from the cloud. Significant non-detections toward a further 3 stars yield robust lower distance limits. The resulting HI mass of Complex C is 4.9^{+2.8}{-2.2} x 10^6 Msun; a total mass of 8.2^{+4.6}{-2.6} x 10^6 Msun is implied, after corrections for helium and ionization. At 10kpc, Complex C has physical dimensions 3x15 kpc, and if it is as thick as it is wide, then the average density is log<n> ~ -2.5. We estimate the contribution of Complex C to the mass influx may be as high as ~0.14 Msun/yr.

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