Given the sample triangle below and the conditions csc b = 10, b = 0.5, find the hypotenuse of the triangle.

a2+b2=c2a2+b2=c2162+52/32=c2162+52/32=c2256+25/9=c2256+25/9=c2258+7/9=c2258+7/9=c2258+7/9−−−−−−−−√=c258+7/9=cc≈16.087

Your sample triangle is missing, but remember that csc stands for cosecant, which is hypotenuse divided by opposite leg. Also,  they tell you b=.5 and we know side b is the opposite leg to angle B since the opposite side is labeled with the same variable as the angle, just in lower case. 10 is the same number as 10/1 so now can set up a proportion of 10/1=H/.5 to solve for the hypotenuse:)