Law of Cosines

Michigan State University - Diagnostic Exam

A triangle has sides of lengths of 4, 5 and 6. The degree measure x of the angle opposite the side of length 6 satisfies which of the following?

a) $x = 90∘$ b) $80 ∘ < x < 90∘$ c) $70∘ < x < 80∘$

d) $60∘ < x < 70∘$ e) $x < 60∘$

Solution:

By the Law of Cosines,

2 2 2 36---16---25- 6 = 4 + 5 - 2(4)(5)cos x ⇒ cos x = - 40 ( ) ⇒ x = cos-1 1- 8 ⇒ x ≈ 82.8∘

Diagnostic:

If you miss this question please review Law of Cosines.

July 15, 2008