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, we can solve for the missing angle C:

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

$11^2 = 7^2 + 10^2 - 2(7)(10)\cos(C)$

$121 = 149 - 140\cos(C)$

$-28 = -140\cos(C)$

$\cos(C) = \frac{-28}{-140} = 0.2$

$C = \cos^{-1}(0.2) \approx 78.46°$ rounded to two decimal places.

Therefore, the best choice is C.

Given a = 7, B = 10, and C =