Question

Campsite A and campsite B are located directlyopposite each other on the shores of Lake Omega,as shown in the diagram below. The two campsitesform a right triangle with Sam's position, S. Thedistance from campsite B to Sam's position is1,300 yards, and campsite A is 1,700 yards from hisposition.what is the distance from campsite A to campsite B,to the nearest yard?

Answer 1

Using Pythagoras theorem

`\begin{gathered} |AS|^2=|AB|^2+|BS|^2 \\ 1700^2=|AB|^2\text{ + }1300^2 \\ 2890000=|AB|^2\text{ + 1690000} \\ |AB|^2=\text{ 2890000-1690000} \\ |AB|^2=1200000 \\ |AB|\text{ = }\sqrt[]{1200000} \\ |AB|\text{ = 1095.45 yards} \\ |AB|\text{ }\cong1095\text{ yards (nearest yard)} \end{gathered}`

Distance from campsite A to campsite B, to the nearest yard is 1095 yards