At a wild-west show, a marksman fires a bullet at a \(12 \mathrm{~g}\) coin that's thrown straight up into the air. The marksman points his rifle at a \(45^{\circ}\) angle above the ground, then fires a \(15 \mathrm{~g}\) bullet at a speed of \(550 \mathrm{~m} / \mathrm{s}\). Just as the coin reaches its highest point, the bullet hits it and glances off, giving the coin an exactly vertical velocity of \(120 \mathrm{~m} / \mathrm{s}\). At what angle measured with respect to the horizontal does the bullet ricochet away from this collision?