Question

A ship sails 14 nautical km due East and 48 nautical km due North. How far is it from the starting point? [2 Marks]

Answer 1

Let the ship start at O and sail due East to A and then due North to B.

Using Pythagoras Theorem we have,

$O{B}^2=O{A}^2+A{B}^2$ [1 Mark]

$O{B}^2={14}^2+{48}^2$

$O{B}^2=(2\times 7{)}^2+(2\times 24{)}^2$

$O{B}^2=2^2(7^2+{24}^2)$

$O{B}^2=2^2\left({25}^2\right).....(7-24-25\text{Pythagoras Triplet})$

$\text{OB}=50\text{cm}$ [1 Mark]