Question Number 198288 by Safojon last updated on 16/Oct/23
Answered by mr W last updated on 17/Oct/23
$$\mathrm{4}+{a}={a}\:\mathrm{cosh}\:\frac{{b}}{\mathrm{2}{a}} \\ $$$$\mathrm{11}={a}\:\mathrm{sinh}\:\frac{{b}}{\mathrm{2}{a}} \\ $$$$\left(\mathrm{4}+{a}\right)^{\mathrm{2}} −\mathrm{11}^{\mathrm{2}} ={a}^{\mathrm{2}} \\ $$$$\Rightarrow{a}=\frac{\mathrm{105}}{\mathrm{8}} \\ $$$$\frac{{b}}{\mathrm{2}{a}}=\mathrm{sinh}^{−\mathrm{1}} \:\frac{\mathrm{11}}{{a}}=\mathrm{sinh}^{−\mathrm{1}} \:\frac{\mathrm{88}}{\mathrm{105}} \\ $$$$\Rightarrow?={b}=\mathrm{2}×\frac{\mathrm{105}}{\mathrm{8}}×\mathrm{sinh}^{−\mathrm{1}} \:\frac{\mathrm{88}}{\mathrm{105}}\approx\mathrm{20}.\mathrm{006}\:{m} \\ $$