In triangle ABC, Side AB=12cm , side BC=17cm and angle ABC=65° . what is the length of side AC?
To find the length of side AC, we can use the Law of Cosines.
The Law of Cosines states: c^2 = a^2 + b^2 - 2ab*cosC, where c is the side opposite angle C, a and b are the other two sides, and C is the angle opposite side c.
In this case, we have side AB = 12 cm (a), side BC = 17 cm (b), and angle ABC = 65° (C). We want to find side AC.
Using the Law of Cosines, we have:
AC^2 = AB^2 + BC^2 - 2*AB*BC*cos(ABC)
AC^2 = 12^2 + 17^2 - 2*12*17*cos(65°)
AC^2 = 144 + 289 - 408*cos(65°)
AC^2 ≈ 590.933
Taking the square root of both sides, we find:
AC ≈ √590.933
AC ≈ 24.290
Therefore, the length of side AC is approximately 24.290 cm.