ariana is standing at the bottom of a hill in the zoo. the angle of elevation from her to the top of the hill is 17 degrees. if the hill if 50 feet tall, how long is the walkway up the hill?​

171.02 ft.

Step-by-step explanation:

Please see the attached image

sin(17)=50/x

x=50/sin(17)≈171.02

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