Question

The hands of a clock are 4cm and 5cm long. Find the distance between the tips of the hands at 16.00h

Answer 1

At 16:00, the hands of the clocks which are 4 cm and 5 cm long can form a triangle with an angle of 120° between them.

Let the tips of the hands are at x distance (in cm) away from each other during this time.

Hence, by law of cosines,

$\displaystyle\longrightarrow\sf {x^2=4^2+5^2-2\times 4\times 5\cos120^{\circ}}$

$\displaystyle\longrightarrow\sf {\underline {\underline {x=\sqrt{61}\ cm}}}$