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Question Number 188119 by mr W last updated on 25/Feb/23

Commented by mr W last updated on 26/Feb/23

$$otherformsof{Heron}^{\prime }sformua.$$$$maybeonedayyoumayusethem.$$

Answered by manxsol last updated on 26/Feb/23

$$otherwaya,b,csidestriangle$$$$A=\frac{1}{2}absin\theta$$$$4A^2=a^2{b}^2{sin}^2\theta$$$$4A^2=a^2{b}^2(1-{cos}^2\theta )$$$$c^2=a^2+b^2-2abcos\theta$$$$cos\theta =\frac{a^2+b^2-c^2}{2ab}$$$$4A^2=a^2{b}^2-a^2{b}^2{\left(\frac{a^2+b^2-c^2}{2ab}\right)}^2$$$$4A^2=a^2{b}^2-\cancel{a^2{b}^2}\frac{{(a^2+b^2-c^2)}^2}{4\cancel{a^2{b}^2}}$$$$16A^2=4a^2{b}^2-(a^2+b^2-c^2)$$$$4A=\sqrt{4a^2{b}^2-{(a^2+b^2-c^2)}^2}$$$$A=\frac{1}{4}\sqrt{4a^2{b}^2-{(a^2+b^2-c^2)}^2}$$$$$$

Commented by mr W last updated on 26/Feb/23

$$correct!$$$$thisformulaisalsogiveninthe$$$$collectioniposted.$$

Commented by manxsol last updated on 26/Feb/23

$$SirW.canyougivemethe$$$$publicationnumber.thanyou$$

Commented by mr W last updated on 26/Feb/23

$$whatisapublicationnumber?$$$$soifieven{don}^{\prime }tknowwhata$$$$publicationnumberis,iwontalso$$$$haveone.$$

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