Given a = 12,b = 14,and c = 7,use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places.
A)80.44°
B)91.02°
C)58.98°
D)29.99°
E)60.33°

Question

Given a = 12,b = 14,and c = 7,use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places. ​
A)80.44°
B)91.02°
C)58.98°
D)29.99°
E)60.33°

Quizplus · Accepted Answer

According to the Law of Cosines:

a^2 = b^2 + c^2 - 2bc cos(A)

Replacing the given values:

12^2 = 14^2 + 7^2 - 2(14)(7) cos(A)

Simplifying:

144 = 317 - 196cos(A)

196cos(A) = 173

cos(A) = 173/196

A = cos^-1(173/196)

A = 58.98° (rounded to two decimal places)

Therefore, the best choice is C.

Given a = 12,b = 14,and C = 7,use the Law