Answer
$$173.35{\text{ft}}$$
Work Step by Step
$$\eqalign{
& B = {\text{12}}0.{\text{7}}^\circ ,a = {\text{127 ft}},c = {\text{69}}.{\text{8 ft}} \cr
& \cr
& {\text{Find }}b,{\text{ use the law of cosines}} \cr
& {b^2} = {a^2} + {c^2} - 2ac\cos B \cr
& {b^2} = {\left( {127} \right)^2} + {\left( {{\text{69}}.{\text{8}}} \right)^2} - 2\left( {{\text{127}}} \right)\left( {{\text{69}}.{\text{8}}} \right)\cos \left( {{\text{12}}0.{\text{7}}^\circ } \right) \cr
& \cr
& {\text{Use a calculator}} \cr
& {b^2} = 30052.5572 \cr
& {\text{Take square roots and choose the positive root}} \cr
& b \approx 173.35{\text{ft}} \cr} $$
