Final answer:
The exact value of cos A when A is √75 is √3/3, found by applying the Pythagorean theorem and simplifying the ratio of the adjacent side over the hypotenuse.
Step-by-step explanation:
Finding Exact Value of cos A
To find the exact value of cos A in simplest radical form when A is √75, we can apply the Pythagorean theorem. The given values represent the sides of a right triangle, with A being the hypotenuse. According to the Pythagorean theorem A = √(Ax² + Ay²), where Ax and Ay represent the lengths of the legs of the right triangle. If Ax = 5 and Ay = √75, then to find cos A, we need to find Ax/A which equals 5/√75. Simplifying this, we get:
cos A = Ax/A = 5/√75 = 5/√(5² · 3) = 5/5√3 = 1/√3 = √3/3 after rationalizing the denominator.
So, the exact value of cos A in simplest radical form when A is √75 is √3/3.