Question

Question #e4968

Answer 1

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