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Question Number 35763 by $@ty@m last updated on 23/May/18

Answered by ajfour last updated on 23/May/18

$$let\mathrm{\angle }BDF=\alpha$$$$AF=30\cos A;AE=36\cos A$$$$\cot \alpha =\frac{AF\cos B+AE\cos C}{BF\sin B-CE\sin C}$$$$=\frac{30\cos A\cos B+36\cos A\cos C}{(18-30\cos A)\sin B-(15-36\cos A)\sin C}$$$$BD=BF\cos B+BF\sin B\cot \alpha$$$$whereBF=18-30\cos A$$$$\cos A,\sin B,\cos B,\sin C,\cos C$$$$canbeevaluatedfromtheknown$$$$valuesofthesidesofthe△ABC.$$

Commented by $@ty@m last updated on 23/May/18

$$Thanksalot!$$

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