The resultant of two forces at right angle is 17N. If the maximum resultant is 23N, the greater force is..

$\text{ when }\theta ={90}^{\circ },\mathrm{F}=17$

$\Rightarrow {\mathrm{F}}_1^2+{\mathrm{F}}_2^2={17}^2....\left(1\right)$

$\text{ When }\theta =0^{\circ },\mathrm{F}=23\Rightarrow {\mathrm{F}}_1+{\mathrm{F}}_2=23....\left(2\right)$

$\text{ consider }{\left({\mathrm{F}}_1+{\mathrm{F}}_2\right)}^2={\mathrm{F}}_1^2+{\mathrm{F}}_2^2+2{\mathrm{F}}_1{\mathrm{F}}_2$

$\Rightarrow {23}^2={17}^2+2{\mathrm{F}}_1{\mathrm{F}}_2.....\left(3\right)$

$\text{ from (2) and (3) }{F}_1=15 ; F_2=8\mathrm{N}.$

$\therefore \mathrm{the} \mathrm{larger} \mathrm{force} \mathrm{is} 15 \mathrm{N}$