Given an isosceles triangle with legs measuring 10 inches and base measuring 18 inches, what is the cosine of one of the base angles?

To find the cosine of one of the base angles in an isosceles triangle, we can use the Law of Cosines. The Law of Cosines states that c² = a² + b² - 2ab*cos(C), where a and b are the sides forming the angle C, and c is the side opposite angle C.

In this case, the sides forming the angle are the legs of the triangle, which measure 10 inches each, and the side opposite the angle is the base of the triangle, which measures 18 inches.

So, we can set up the equation as follows:

18² = 10² + 10² - 21010*cos(C)

Solving for cos(C), we get:

cos(C) = (10² + 10² - 18²) / (21010)

cos(C) = (100 + 100 - 324) / 200

cos(C) = -0.24

So, the cosine of one of the base angles in the given isosceles triangle is -0.24.