if the three sides of a triangle is 4,5,6 then the cosine of the angle between the sides 4 and 5 is
cos ยค = (4^2 + 5^2 - 6^2)/(2*4*5)
To find the cosine of the angle between the sides of a triangle, you can use the Law of Cosines. The Law of Cosines states that in any triangle with sides a, b, and c, and the angle opposite side c denoted by angle C, the following equation holds true:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we are given that the three sides of the triangle are 4, 5, and 6, and we need to find the cosine of the angle between the sides 4 and 5.
Let's call the angle between sides 4 and 5 as angle A. Therefore, the side opposite angle A is 6.
Using the Law of Cosines, we can rewrite the equation as:
6^2 = 4^2 + 5^2 - 2 * 4 * 5 * cos(A)
Simplifying this equation:
36 = 16 + 25 - 40 * cos(A)
36 = 41 - 40 * cos(A)
Rearranging this equation:
40 * cos(A) = 41 - 36
40 * cos(A) = 5
cos(A) = 5/40
cos(A) = 1/8
Therefore, the cosine of the angle between the sides 4 and 5 is 1/8.