Question

Your friend is trying to calculate the height of a nearby oak tree. You tell him that you learned how to use similar triangles in Geometry class. You tell your friend to measure his height (75 inches) and you measure the length of his shadow (48 inches). Both of you measure the length of the tree’s shadow (38 feet). How tall is the tree (in feet)? Round to the nearest hundredth.

Answer 1

59.38 ft

Explanation:

The person and his shadow form a triangle. The tree and its shadow also form a triangle. The triangles are similar triangles, so the lengths of corresponding sides are proportional.

Let the unknown tree height be h.

(person's height)/(person's shadow) = (tree height)/(tree's shadow)

(75 in.)/(48 in.) = h/(38 ft)

(25)/(16) = h/(38 ft)

16h = 25 * 38 ft

16h = 950 ft

h = 59.375 ft

h = 59.38 ft