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Question Number 92269 by Power last updated on 05/May/20

Answered by mr W last updated on 05/May/20

$$letBD=1$$$$\frac{AB}{\sin 51}=\frac{BD}{\sin (25+51)}$$$$\Rightarrow AB=\frac{\sin 51}{\sin 76}$$$$\frac{BC}{\sin 99}=\frac{BD}{\sin (15+99)}$$$$\Rightarrow BC=\frac{\sin 99}{\sin 114}$$$${AC}^2={\left(\frac{\sin 51}{\sin 76}\right)}^2+{\left(\frac{\sin 99}{\sin 114}\right)}^2-2\left(\frac{\sin 51}{\sin 76}\right)\left(\frac{\sin 99}{\sin 114}\right)\cos (24+15)$$$$AC\approx 0.681$$$$BF/AC\approx 1.467$$$$\frac{\sin x}{BC}=\frac{\sin (24+15)}{AC}$$$$\sin x=\frac{\sin 99}{\sin 114}\times \frac{\sin 39}{AC}=1$$$$\Rightarrow x=90°$$

Commented by Power last updated on 05/May/20

$$\mathrm{thanks}$$

Commented by otchereabdullai@gmail.com last updated on 05/May/20

$$\mathrm{powerful}$$

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