At a certain time of day, the angle of elevation of the sun is 30°. a tree has a shadow that is 25 feet long. find the height of the tree to the nearest foot.
a)
13 ft
b)
14 ft
c)
22 ft
d)
29 ft

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