Question

I could use some help solving these two problems if possible. Thank you.

Answer 1

iven the figure below:

Where

`\begin{gathered} S\Rightarrow satellite \\ B\Rightarrow Bora-Bora \\ G\Rightarrow Greenland \\ R\Rightarrow Rapa\text{ Nui} \\ H\Rightarrow St.\text{ Helen} \end{gathered}`

Using the secant-secant theorem expressed as

`SB\left(SB+BG\right)=SR\left(SR+RH\right)\text{ ----- equation 1}`

Given that th e satellite signal reaches Bora-Bora at 38,000 km and Greenland which is an additional 20,000km, this implies that

`\begin{gathered} SB=38000 \\ BG=20000 \end{gathered}`

If the distance from the satellite to Rapa Nui is 45,000 km, this implies that

`SR=45000`

The total distance from the satelite to St. Helen is expressed as

`SH=SR+RH\text{ ----- equation 2}`

From equation 1,

`\begin{gathered} \begin{equation*} SB\left(SB+BG\right)=SR\left(SR+RH\right)\text{ } \end{equation*} \\ substitute\text{ equation 2 into equation 1} \\ thus,\text{ we have} \\ SB\left(SB+BG\right)=SR\left(SH\right)\text{ ---- equation 3} \end{gathered}`

Substituting the values, we have

`\begin{gathered} 38000\left(38000+20000\right)=45000\left(SH\right) \\ \Rightarrow38000*58000=45000\left(SH\right) \end{gathered}`

divide both sides by 45000,

`\begin{gathered} SH=(38000*58000)/(45000) \\ \Rightarrow SH=48977.77777 \end{gathered}`

Hence, the signal will travel a distance of 48977.77777 km from the satellite to St. Helen.