To approximate the length of a lake, surveryor starts at one end of the lake and walks 156 yards. He then turns 110° and walk 198 yards until he arrives at the other end of the lake. Approximately how long is the lake? (round to nearest yard)

Answer 1

We can use the Law of Cosines to approximate the length of the lake. Here's how:

Let's call the distance we're trying to find "x". We know two sides and the included angle of the triangle formed by the starting point, ending point, and the point where the surveyor turned. Using the Law of Cosines, we have:

x^2 = 156^2 + 198^2 - 2(156)(198)cos(110°)

x^2 = 24336 + 39204 - (61848)(-0.34202)

x^2 = 63596.79915

x ≈ 252.16 yards

Therefore, the lake is approximately 252 yards long.