Find the height of the shooting star from the Earth's ground
This is basically a trigonometry question.  I wasn't sure from the question if the apparent location from your friend's position was six degrees higher or lower.  I chose higher for the example, but you could change it.


You have two triangles with the same altitude, but different bases and angles.

$$\text{altitude} = x \tan(81^{\circ}) = (x + 20km) \tan (75^{\circ})$$  Do you see how to calculate it from there?