In class the following result was derived 8 = (n-1) R 2h for the angle of "dip" or "rise" in an extraterrestrial mirage near the horizon, where n = 1.00026, where 8 is the angle (in degrees). This derivation was based on the approximation coso ~ 1. Now rederive a better approximation to & based on the better approximation coso ~ 1 - 82/2. This will of course result in a quadratic equation for 8. Justify mathematically which root should be chosen for 8. Then calculate the value of & in degrees (to 2 significant figures) based on this new approximation. You may assume as before that R ~ 6400 km and h ~ 8 km. 2ind order