Use the Law of Cosines to find the missing angle. Find m∠B, given a = 11, b = 12, and c = 17.
Mathematics · High School · Tue Nov 03 2020
Answered on
Given:
a = 11, b = 12, and c = 17.
Find: m∠B
Law of cosine formulas:
c^2 = a^2 + b^2 - 2ab cos c
b^2 = a^2 +c^2 - 2ac cos b
cos b = (a^2 + c^2 - b^2)/2ac
Solution:
Substitute the given values of a, b and c .
cos b = (a^2 + c^2 - b^2)/2ac
cos b = ( (11)^2 + (17)^2 - (12)^2 ) /2 (11)(17)
cos b = ( 121 + 289 - 144) / 374
cos b = 266/374
cos b = 0.71
In order to determine the angle, we take the arc cosine of b. arc cosine is denoted as cos ^ -1
b= cos^-1 (0.71)
b = 44.77°
m∠B = 44.77°