Precalculus Find Distance Using this Info

Question

To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. (Assume points A and B are exactly along the shoreline, and that a = 2.52 miles and b = 3.51 miles. Round your answer to two decimal places.)

 

mi

Answer 1

Let side AB = x

Use the Law of Cosines:

x² = a² + b² - 2abcos(C)

x² = 2.52² + 3.51² - 2(2.52)(3.51)cos(40.3°)

x² = 6.3504 + 12.3201 - 17.6904cos(40.3°)

x² = 18.6705 - 17.6904(0.762668)

x² = 5.1786

x = √5.1786

x = 2.28 miles