Given for a ABC with usual notation. If then the ordered tri... | JEE Main 2020 Properties of Triangle | JEE Main - Mathematicon

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Properties of Triangle

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Given ${{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}$ for a $\Delta$ ABC with usual notation. If ${{\cos A} \over \alpha } = {{\cos B} \over \beta } = {{\cos C} \over \gamma },$ then the ordered triad ( $\alpha$ , $\beta$ , $\gamma$ ) has a value :

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Solution

b + c = 11 $\lambda$ , c + a = 12 $\lambda$ , a + b = 13 $\lambda$ $\Rightarrow$ a = 7 $\lambda$ , b = 6 $\lambda$ , c = 5 $\lambda$ (using cosine formula) cosA = ${1 \over 5},$ cosB = ${19 \over 35},$ cosC = ${5 \over 7},$ $\alpha$ : $\beta$ : $\gamma$ $\Rightarrow$ 7 : 19 : 25

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