Answer:
296.1 yards
Explanation:
The surveyor is interested in solving a triangle with two sides and the enclosed angle known. The Law of Cosines is used for that purpose.
The angle interior to the triangle where the surveyor turned is the supplement of the turning angle:
180° -110° = 70°
The law of cosines tells us the relation of the given sides (a, b) and angle (C) to the unknown side (c) is ...
c² = a² +b² -2ab·cos(C)
c² = 245² +270² -2·245·270·cos(70°) ≈ 87675.7350
c ≈ √87675.7350 ≈ 296.10
The length of the lake is about 296.1 yards.