In ΔFGH, the measure of ∠H=90°, GF = 89, HG = 80, and FH = 39. What ratio represents the cotangent of ∠F?

"if it is my birthday, then it is snowing"

y=3n + 1

step-by-step explanation:

this is wrong because it says the second number is one less and i added one instead

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