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

I could use some help solving these two problems if possible. Thank you.-example-1
User Pritha
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1 Answer

2 votes

Solution:

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.

I could use some help solving these two problems if possible. Thank you.-example-1
User Tuxxi
by
8.4k points

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