A spruce tree is approximately the shape of a cone with a slant height of 20 ft. The angle formed by the tree with the ground measures 72º. Estimate the height of the tree. Round to the nearest foot.

We have a triangle, when:

hypotenuse=slant height=20 ft

opposite side=height of the tree=?

angle formed by the tree with the ground=72º

sin Ф=opposite / hypotenuse ⇒ opposite = (hypotenuse) (sin Ф)

In this case:

oppssite=20 ft / sin 72º=19.021 ... ≈19

Answer: the heigth of the tree is 19 ft.