A 24 foot tall tree casts a shadow that is 18 foot long. At the same time, Nathan casts a 4-foot shadow. How tall is Nathan?
Using similar triangles, we can set up the proportion:
(Height of tree)/(Length of tree's shadow) = (Height of Nathan)/(Length of Nathan's shadow)
Plugging in the given values:
(24 ft)/(18 ft) = (Height of Nathan)/(4 ft)
Cross multiplying:
(24 ft)*(4 ft) = (18 ft)*(Height of Nathan)
96 ft = 18 ft * (Height of Nathan)
Dividing both sides by 18 ft:
(96 ft)/(18 ft) = Height of Nathan
Simplifying:
5.33 ft = Height of Nathan
Therefore, Nathan is approximately 5.33 feet tall.