Question #e4968

1 Answer
Apr 3, 2016

The line AH is tangential to the earth's surface, hence angle AHO will be 90^0900

Angle HAO will be (90^0-2.23^0)(9002.230), so angle HOA will be 2.23^02.230

We know that:
- line OH has length rr, and
- line OA has length r+4.83kmr+4.83km

We can now use the cosine rule in relation to angle HOA
cos2.23^0=r/(r+4.83) ="adjacent"/"hypotenuse"cos2.230=rr+4.83=adjacenthypotenuse

rearranging to find rr:

(r+4.83)*cos2.23^0=r(r+4.83)cos2.230=r

r*cos2.23^0+4.83*cos2.23^0=rrcos2.230+4.83cos2.230=r

4.83*cos2.23^0=r -r*cos2.23^04.83cos2.230=rrcos2.230

4.83*cos2.23^0=r(1 -cos2.23^0)4.83cos2.230=r(1cos2.230)

(4.83*cos2.23^0)/(1 -cos2.23^0)=r4.83cos2.2301cos2.230=r

Using the above in a calculator gives r=6,373km