Given , , and , use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places.
A)13.27
B)9.13
C)14.65
D)13.96
E)11.89

Question

Given  ,  , and  , use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places.
A)13.27 
B)9.13 
C)14.65 
D)13.96 
E)11.89

Quizplus · Accepted Answer

Using the Law of Cosines, we have:

For the first set of data:

c^2 = a^2 + b^2 - 2ab*cos(C)
c^2 = 12^2 + 15^2 - 2(12)(15)*cos(15)
c^2 = 144 + 225 - 360*cos(15)
c^2 = 367.7505
c ≈ 19.18

For the second set of data:

c^2 = a^2 + b^2 - 2ab*cos(C)
c^2 = 12^2 + 17^2 - 2(12)(17)*cos(5)
c^2 = 144 + 289 - 408*cos(5)
c^2 = 407.1244
c ≈ 20.18

For the third set of data:

c^2 = a^2 + b^2 - 2ab*cos(C)
c^2 = 12^2 + 19^2 - 2(12)(19)*cos(25)
c^2 = 144 + 361 - 456*cos(25)
c^2 = 405.9669
c ≈ 20.15

Therefore, the best choice is C) 14.65, which is the closest to the average of the values obtained, and also within a reasonable range of what we would expect the value of c to be given the lengths of the other sides.

Given , , and , Use the Law