law of cosines

Question

use the law of cosines to find angle measure.

a = 9

b = 10

c = 11

Find the measure of Angle(A) ? 

 

Answer 1

We want to find the measure of angle A, so let's write the law of cosines in terms of side a.

a² = b² + c² - 2bc cos (A)

Rearrange to get         2bc cos (A) = b² + c² - a²

so,                             A = cos^-1[ (b² + c² - a²) / 2bc]

substitute values a, b, and c to get           A = cos^-1(140/220) = 50.48 degrees.

Answer 2

a² = b² + c² - 2bc · cos(A)
81 = 100 + 121 - 220 · cos(A) ---> -140 = -220 · cos(A)
cos(A) = -140 / (-220) ---> A = 50.48⁰