Tie a balloon to the ground next to a mountain. You will notice that the balloon leans towards the mountain.
Um... you really think I'll notice that?
Let's be generous and imagine the mountain as a hemisphere of diameter equal to the base diameter of the mountain. Let's now figure out the gravitational force that a sphere of this diameter would have on a nearby balloon, and halve that force.
Say the mountain is a cone with a base diameter of 5000 m and made of granite with an average density of 2.75 g/cm^3. I'm not a geologist, so feel free to offer different numbers.
The sphere would have a volume of V = 4/3 π r^3 ~ 26180000 m^3. At an average density of 2.75 g/cm^3, or 2750 kg/m^3, this amounts to about 71,995,000,000 kg, or M = 35,997,500,000 kg for the hemisphere.
The balloon weighs, say, 100 g or m = 0.1 kg.
Let's place the balloon a meter away from the base of the mountain, so that r = 2501 m.
The force of gravity, then, between the balloon and the mountain is, according to Newton,
F = G M m / r^2 = (6.6742 x10^-11 N m^2 / kg^2) * (35,997,500,000 kg) * (0.1 kg) / (6255001 m^2)
= 3841.0 x10^-11 N or approximately 3.9194 x10^-9 g.
In other words, the force is about four
billionths of the force due to Earth's gravity... and this is a generous estimate.
No angle will be visible.