The cosine of the angle in a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse. This means that the cosine of the angle A is equal to the ratio of the adjacent leg AH to the hypotenuse AC.
cos A = AH / AC.
In an isosceles triangle, the height drawn to the base is also both the bisector and the median. Means:
AH = HB = 25/2 = 12.5.
Let’s find the AS according to the Pythagorean theorem:
AC² = CH² + AH²;
AC² = 15² + 12.5²;
AC² = 225 + 156.25;
AC² = 381.25;
AC = √381.25;
cos A = 12.5 / √381.25 = 12.5 / 19 √ 20.25.
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