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Question Number 67860 by TawaTawa last updated on 01/Sep/19

Commented by TawaTawa last updated on 01/Sep/19

$$\mathrm{Find}\mathrm{angle}\mathrm{a}$$

Commented by mr W last updated on 01/Sep/19

$$a=72°$$

Commented by TawaTawa last updated on 01/Sep/19

$$\mathrm{Correct},\mathrm{please}\mathrm{workings}\mathrm{sir}$$

Answered by mr W last updated on 01/Sep/19

$$letBC=1$$$$\mathrm{\angle }B=12+36=48=30+18=\mathrm{\angle }C$$$$\Rightarrow AB=AC=\frac{BC}{2}\times \frac{1}{\cos \mathrm{\angle }B}=\frac{1}{2\cos 48°}$$$$\frac{BD}{\sin 30°}=\frac{BC}{\sin (12+30)}=\frac{1}{\sin 42°}=\frac{1}{\cos 48°}$$$$\Rightarrow BD=\frac{1}{2\cos 48°}=BA$$$$2a+36=180$$$$\Rightarrow a=\frac{180-36}{2}=72°$$

Commented by TawaTawa last updated on 01/Sep/19

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

Commented by TawaTawa last updated on 02/Sep/19

$$\mathrm{Sir},\mathrm{why}\mathrm{did}\mathrm{you}\mathrm{let}\mathrm{BC}=1,\mathrm{and}\mathrm{when}\mathrm{can}\mathrm{i}\mathrm{use}\mathrm{it}\mathrm{in}\mathrm{question}.$$

Commented by mr W last updated on 03/Sep/19

$$youcanalsoletBC=aifyoulike.if$$$$youareonlyinterestedatangles,the$$$$absolutevaluesofthelengthesarenot$$$$important,onlytheratiobetweenthem.$$

Commented by TawaTawa last updated on 06/Sep/19

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

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