In triangle ABC, angle c is a right angle. if cos A= 5/8, what is the value of cos B? A. 3/8
B. 5/3
C. sqrt 39/8
D. sqrt 89/8
with explanation pls

C. sqrt 39/8

Step-by-step explanation:

To solve this, we need to first draw the triangle.

cos Ф = adjacent / hypotenuse

cos A = 5/8 = adjacent / hypotenuse

From the diagram, when dealing with angle A,      AB= hypotenuse = 8 and AC=adjacent =5

But when we are dealing with angle B , then BC becomes the adjacent and AC  will now be the opposite, but AB still remains the hypotenuse, which implies, if we are looking for the value of COS B , we need to find side BC, we can easily do that using the Pythagoras theorem;

adjacent² + opposite² = hypotenuse²

adjacent² =  hypotenuse² - opposite²

  BC²        = AB² -  AC²

                =8² -  5²

                = 64 - 25

              = 39

BC =√39

adjacent = √39       hypotenuse =8

cos B = adjacent / hypotenuse

cos B  = √39 / 8