Right-angled Triangles, SM-Bank 043

Arthur observes a plane through his binoculars at a distance of 7500 metres. If Ben is directly under the plane and it is flying at an altitude of 5000 metres, how far apart are Arthur and Ben? Give your answer correct to the nearest metre. (2 Marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

\(5590\ \text{m}\)

Show Worked Solution

\(\text{Using Pythagoras’ Theorem: }\ \ a^2+b^2=c^2\)

\(\text{Let }\ a=d,\ b=5000,\ c=7500\)

\(d^2+5000^2\)	\(=7500^2\)
\(d^2\)	\(=7500^2-5000^2\)
\(d^2\)	\(=31\ 250\ 000\)
\(d\)	\(=5590\dots\)
\(d\)	\(\approx 5590\)

\(\therefore\ \text{Arthur and Ben are approximately }5590\ \text{metres apart}.\)