A triangle has two sides that measure 2.5 cm and 16.5 cm. Which could be the measure of the third side?

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Answer 1 · 2016-12-08T07:28:38

Third side will have a value between $14$ and $19$ .

As the two sides measure $2.5$ $cm.$ and $16.5$ $cm.$ , let the included angle between them be $theta$ .

It is evident that $0^o < theta < 180^o$ .

Then using the cosine formula of solving triangles,

the square on the third side will be given by

$2.5^2+16.5^2-2xx2.5xx16.5xxcostheta$

$=6.25+272.25-82.5costheta$

$=278.5-82.5costheta$

and as $0^o < theta < 180^o$ , $-1 < costheta < 1$

Hence the third side say $x$ will be given by

$sqrt(278.5-82.5) < x < sqrt(278.5+82.5)$

or $sqrt196< x< sqrt361$

or $14 < x <19$ .

Hence third side will have a value between $14$ and $19$ .