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Question Number 61449 by Tawa1 last updated on 02/Jun/19

Commented by Tawa1 last updated on 02/Jun/19

$$\frac{{\mathrm{a}}^2+{\mathrm{b}}^2}{{\mathrm{c}}^2}=?$$

Answered by perlman last updated on 02/Jun/19

$$\frac{c}{sin\left(30\right)}=\frac{a}{sin\left(140\right)}=\frac{b}{sin\left(130\right)}$$$$b=\frac{sin\left(130\right)}{sin\left(30\right)}c$$$$a=\frac{sin\left(140\right)}{sin\left(30\right)}c$$$$\frac{a^2+b^2}{c^2}=\frac{{sin}^2\left(130\right)+{sin}^2\left(140\right)}{{sin}^2\left(30\right)}=4({sin}^2\left(130\right)+{sin}^2\left(140\right))=4({sin}^2(180-50)+{sin}^2(90+50))$$$$=4{sin}^2\left(50\right)+4{cos}^2\left(50\right)=4({sin}^2\left(50\right)+{cos}^2\left(50\right))=4\times 1=4$$$$$$

Commented by Tawa1 last updated on 02/Jun/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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