Find the arc length of the partial circle.
Either enter an exact answer in terms of it or use 3.14 for it and enter your answer as a decimal.
units

The length of the arc is 18.84 u

Step-by-step explanation:

First of all we have to calculate the entire circumference

To solve this problem we need to use the circumferenc formula of a circle:

c = circumference

r = radius = 4

π = 3.14

c = 2π * r

we replace with the known values

c = 2 * 3.14 * 4

c = 25.12 u

The length of the circumference is 25.12 u

we have a partial circle of 270 ° so we have to divide it by 360 ° to know what fraction of the whole circle represents

270° / 360° = 3/4

25.12u * 3/4 = 18.84 u

The length of the arc is 18.84 u

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