Question #e4968

1 Answer
Apr 3, 2016

The line AH is tangential to the earth's surface, hence angle AHO will be 900

Angle HAO will be (9002.230), so angle HOA will be 2.230

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
cos2.230=rr+4.83=adjacenthypotenuse

rearranging to find r:

(r+4.83)cos2.230=r

rcos2.230+4.83cos2.230=r

4.83cos2.230=rrcos2.230

4.83cos2.230=r(1cos2.230)

4.83cos2.2301cos2.230=r

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