Rick's scores in his last 15 rounds of golf are 72, 80, 75, 84, 78, 72. 75, 68, 81, 74, 79, 70, 77, 83, and 72. If he scores an 80 on each of the next three rounds, which measure of center would increase
more, the mean or median? Justify your answer.

what is the answer?

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

h= 12 inches

step-by-step explanation: