Law of Cosines

Michigan State University - Diagnostic Exam

The triangle $Δ ABC$ has sides of length a = 8, b = 15, and c = 12. $∠ A$ is closest to which of the following?

a) $63 ∘$ b) $148∘$ c) $32 ∘$ d) $25∘$ e) none of these

Solution:

By the Law of Cosines,

2 2 2 64---225---144- 8 = 15 + 12 - 2 (15 )(12 )cosA ⇒ cosA = - 360 ( ) ⇒ A = cos- 1 61- 72 ⇒ A ≈ 32 ∘

Diagnostic:

If you miss this question please review inverse trigonometric functions.

July 15, 2008