To approximate the length of a marsh a surveyor walkes x 37

To approximate the length of a marsh, a surveyor walkes x = 370 meters from point A to point B, then turns 75 degree and walks 220 meters to point C. Approximate the length AC of the marsh. Determine the angle theta in the design of the streetlight shown in the figure, where x = 2.

Solution

from the figure angle B=180^o-75^o=105^o

c=x =370m

a=220m

length AC= b

by law of cosines

b²=a²+c²-2accosB

b²=220²+370²-(2*220*370*cos105^o)

b²=227435.74

b=476.9

length AC of the marsh =476.9 m