Two tugboats that are a = 100 ft apart pull a barge, as shown. If the length of one cable is b = 206 ft and the length of the other is c = 235 ft, find the angle formed by the two cables. (Round your answer to the nearest degree.)
we know that
The law of cosines states that
a^2=b^2+c^2-2(b)(c)cos(A)
In this problem we have
a=100 ft
b=206 ft
c=235 ft
A ----> is the angle formed by the two cables
substitute the given values in the formula
100^2=206^2+235^2-2(206)(235)cos(A)
Solve for cos(A)
2(206)(235)cos(A)=206^2+235^2-100^2
2(206)(235)cos(A)=87,661
cos(A)=0.9054
using a calculator
therefore
the answer is 25 degrees
