Question

Will likes to skate at a game store that is due south of his school and due west of his favoriteice cream parlor. If the game store is 6 miles from his school and the straight-line distancebetween the school and the ice cream parlor is 10 miles, how far is the game store from theice cream parlor?

Answer 1

So we will firt sketch the given information

Let S denotes the location of the school

Let G denotes the location of the game store

Let I denotes the location for his favourite ice cream palor

It is clear from the diagram above that we want to find x

Using the pythagoras theorem

`\text{hyp}^2=\text{opp}^2+\text{adj}^2`

Subtituting

`\begin{gathered} 10^2=6^2+x^2 \\ 100=36+x^2 \\ x^2=100-36 \\ x^2=64 \\ x=\sqrt[]{64} \\ x=8 \end{gathered}`

The distance between the game store and the ice cream parlor is 8 miles