Given the sample triangle below and the conditions cosb=4/5, a=10 , find the hypotenuse of the triangle.

See the attached figure
For the shown right triangle at C

cos B = a/c = a / hypotenuse 
∵ cos B = 4/5    and    a = 10

∴ 4/5 = 10/c  
∴ c = 10/(4/5) = 10 * 5/4 = 12.5

∴ The hypotenuse of the triangle = 12.5