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Question Number 146457 by mathdanisur last updated on 13/Jul/21

Commented by mathdanisur last updated on 13/Jul/21

$$findx=?$$

Answered by gsk2684 last updated on 13/Jul/21

$$let\mathrm{\angle }BAC=\theta$$$$usingcosinerule$$$$7^2=x^2+2^2-2.x.2.\cos ({90}^0+\theta )$$$$49=x^2+4+4x\sin \theta$$$$45=x^2+4x\left(\frac{x}{23}\right)$$$$45\times 23=23x^2+4x^2$$$$x^2=\frac{45\times 23}{27}=\frac{115}{3}$$$$x=\sqrt{\frac{115}{3}}$$

Commented by mathdanisur last updated on 13/Jul/21

$$thankyouSercool$$

Answered by mr W last updated on 15/Jul/21

$$x^2=2^2+7^2-2\times 2\times 7\cos D...\left(i\right)$$$${23}^2-x^2={25}^2+7^2-2\times 25\times 7\cos D...\left(ii\right)$$$$\left(i\right)\times 25-\left(ii\right)\times 2:$$$$25x^2-2\times {23}^2+2x^2=25(2^2+7^2)-2({25}^2+7^2)$$$$27x^2=45\times 23$$$$x=\frac{\sqrt{345}}{3}$$

Commented by mathdanisur last updated on 19/Jul/21

$$thankyouSer,butanswer:\frac{\sqrt{115}}{3}$$

Commented by mr W last updated on 20/Jul/21

$$youshouldcheckbeforeyousay!$$$$whereiswronginmyworking?$$$$myansweris\frac{\sqrt{345}}{3}.ifyoumeanthe$$$$answeris\sqrt{\frac{115}{3}},then\frac{\sqrt{345}}{3}isalso$$$$right.$$

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