Question

in triangle ABC , given below AB=8 cm BC= 6 CM and AC= 3cm . calculated the length of OC.

Answer 1

Using Pythagoras theorem, In a Rightangled triangle $AOC$ we have

${AO}^2+{OC}^2={AC}^2$

$\Rightarrow y^2+x^2=3^2$

$\therefore y^2=9-x^2$ .......$\left(1\right)$

Using Pythagoras theorem, In a Rightangled triangle $AOB$ we have

${AO}^2+{OB}^2={AB}^2$

$\Rightarrow y^2+{(x+6)}^2=8^2$

$\Rightarrow 9-x^2+x^2+12x+36=64$

$\Rightarrow 12x+45=64$

$\Rightarrow 12x=64-45=19$

$\Rightarrow x=\frac{19}{12}=1.58$cm

Hence $OC=1.58$cm