#### Answer

134.7 cm

#### Work Step by Step

1. Split an isosceles triangle into two equal right triangles, with angle $34^{\circ}22'$ (halved angle of the isosceles triangle ) and opposite side $92.1 cm$ (halved base of the isosceles triangle )
2. To find x (adjacent) use definition of trig function tangent
$\tan 34^{\circ} 22 ' = \frac{92.1}{x}$
$x\approx 134.7$ [4 significant figures as it is in a given side]