Hyperbolic Metamaterials (HMMs) have recently garnered much attention because they possess the ability for broadband manipulation of the photon density of states and sub-wavelength light confinement. However, a major difficulty arises with the coupling of light out of HMMs due to strong confinement of the electromagnetic field in states with high momentum called high-k modes which become evanescent outside the structure. Here we report the first demonstration of directional out-coupling of light from high-k modes in an active HMM using a high index bulls-eye grating. Quantum dots (QDs) embedded underneath the metamaterial show highly directional emission through the propagation and out-coupling of resonance cones which are a unique feature of hyperbolic media. This demonstration of efficient out-coupling of light from active HMMs could pave the way for developing practical photonic devices using these systems.