Question Number 43980 by Tawa1 last updated on 19/Sep/18
Answered by MJS last updated on 19/Sep/18
$${a}=\mathrm{2}+\mathrm{5}=\mathrm{7} \\ $$$$\alpha=\mathrm{60}° \\ $$$$ \\ $$$${b}=\mathrm{2}+{p} \\ $$$${c}=\mathrm{5}+{p} \\ $$$$ \\ $$$${a}^{\mathrm{2}} ={b}^{\mathrm{2}} +{c}^{\mathrm{2}} −\mathrm{2}{bc}\mathrm{cos}\:\alpha \\ $$$${p}^{\mathrm{2}} +\mathrm{7}{p}−\mathrm{30}=\mathrm{0} \\ $$$${p}=−\frac{\mathrm{7}}{\mathrm{2}}\pm\frac{\mathrm{13}}{\mathrm{2}}\:\wedge\:{p}>\mathrm{0}\:\Rightarrow\:{p}=\mathrm{3} \\ $$$$ \\ $$$${a}=\mathrm{7} \\ $$$${b}=\mathrm{5} \\ $$$${c}=\mathrm{8} \\ $$$$ \\ $$$${r}=\sqrt{\frac{\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)}{{s}}}\:\:\mathrm{with}\:{s}=\frac{{a}+{b}+{c}}{\mathrm{2}} \\ $$$${s}=\mathrm{10}\:\Rightarrow\:{r}=\sqrt{\mathrm{3}} \\ $$
Commented by Tawa1 last updated on 19/Sep/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\: \\ $$
Commented by Tawa1 last updated on 19/Sep/18
$$\mathrm{sir}\:\mathrm{i}\:\mathrm{thought}\:\:\mathrm{p}\:=\:−\:\mathrm{10}\:\:\mathrm{or}\:\:\mathrm{3}. \\ $$$$\mathrm{How}\:\mathrm{is}\:\mathrm{it}\:\mathrm{10}\:\mathrm{sir}\:??\:\:\mathrm{why}\:\mathrm{not}\:\mathrm{3}\:\mathrm{sir}?? \\ $$
Commented by MJS last updated on 19/Sep/18
$$\mathrm{you}'\mathrm{re}\:\mathrm{right},\:\mathrm{let}\:\mathrm{me}\:\mathrm{correct}... \\ $$$$\mathrm{here}\:\mathrm{you}\:\mathrm{see}\:\mathrm{it}'\mathrm{s}\:\mathrm{better}\:\mathrm{to}\:\mathrm{think}\:\mathrm{than}\:\mathrm{to}\:\mathrm{copy}/\mathrm{paste} \\ $$