Question #e4968

1 Answer
Apr 3, 2016

The line AH is tangential to the earth's surface, hence angle AHO will be 90^0

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

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

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

rearranging to find r:

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

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

4.83*cos2.23^0=r -r*cos2.23^0

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

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

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