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

step-by-step explanation:

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.