<PRE><B>Question 24655</B>
a picture always helps
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35 km N
65 km east
north and east are at right angles to eachother, so use the pythagorean theorem
which says hypoteneuse= {{{sqrt(x^2 + y^2)}}}
where x and y are the legs of the right triangle
{{{H = sqrt(35^2 + 65^2)}}}
note that 35^2 = (5 * 7)^2 = 5^2 * 7^2
and also  65^2 = (5 * 13)^2 = 5^2 * 13^2
{{{H = (sqrt(5^2)) * sqrt(7^2 + 13^2)}}}
{{{H = 5 * sqrt(49 + 169)}}}
{{{H = 5 * sqrt(218)}}}
calculate this for the answer  </PRE>