Cardboard Inc. makes rectangular boxes for frozen dinners. The dimensions of the box need to be 5in x 8.8in x 10in. How much cardboard is needed to create the box?

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

the answer is c: divide the arc's degree measure by 360°, then multiply by the circumference of the circle.