1.5 The Cosine Law To use the cosine law, we must know: • The measure of two sides and one angle, or The Cosine Law For a side: !
!
!
𝑐 = 𝑎 + 𝑏 − 2𝑎𝑏𝑐𝑜𝑠𝐶 !
!
The measures of all three sides For an angle: 𝑐𝑜𝑠𝐶 =
!
𝑏 = 𝑎 + 𝑐 − 2𝑎𝑐𝑐𝑜𝑠𝐵 𝑐𝑜𝑠𝐵 =
!
!
!
𝑎 = 𝑏 + 𝑐 − 2𝑏𝑐𝑐𝑜𝑠𝐴 𝑐𝑜𝑠𝐴 =
! ! ! ! ! ! ! !
!!!" ! ! ! ! ! ! ! !
!!!" ! ! ! ! ! ! ! !
!!!" Example 1) In ∆ABC, a = 7.2cm, b = 3.6 cm and c = 5.0 cm. Determine the measure of angle A to the nearest degree. Example 2) To determine the length of a small lake, a surveyor takes measurements. From a point, C, the distances to points A and B at the ends of the lake are 854 m and 788m. The angle between the lines of sight to the two points is 107°. Determine the length of the lake.