Given a = 7,b = 10,and c = 11,use the Law of Cosines to solve the triangle for the value of С.Round your answer to two decimal places. Figure not drawn to scale
A)62.96°
B)80.44°
C)78.46°
D)38.57°
E)60.33°

Question

Given a = 7,b = 10,and c = 11,use the Law of Cosines to solve the triangle for the value of С.Round your answer to two decimal places.  Figure not drawn to scale
A)62.96° 
B)80.44° 
C)78.46° 
D)38.57° 
E)60.33°

Quizplus · Accepted Answer

Using the Law of Cosines:

$c^2=a^2+b^2-2ab\cos C$

$11^2=7^2+10^2-2\cdot7\cdot10\cos C$

$121=149-140\cos C$

$-28=-140\cos C$

$\cos C=\frac{-28}{-140}=\frac{1}{5}$

$C=\cos^{-1}\left(\frac{1}{5}\right)\approx78.46°$

The answer is C, which is approximately 78.46°.

Given a = 7,b = 10,and C = 11,use the Law