The figure below shows a triangular piece of cloth: triangle abc has angle abc equal to 90 degrees and angle bac equal to 38 degrees. length of ac is 5 inches. what is the length of the portion bc of the cloth?

answer: 3.078 inches.

step-by-step explanation:

based on the information provided, the triangle is like the one shown in the image attached.

then, in order to find the lenght of bc, you need to apply the following identity:

in this case:

now you can substitute values and solve for bc:

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

answer is because 4×10=40

and 98×4= is 392

40,392