Geometry homework question.

Question

A tree casts a shadow 1600 cm long. At the same time, the shadow cast by a 34 cm tall statue is 96 cm long. Find the height of the tree rounded to the nearest hundredths.

Answer 1

The tree & shadow and the statute & shadow essentially create two sets of corresponding sides of similar triangles. They are similar because they share the same angle created by the sun's rays on the objects. Similar triangles' corresponding sides are proportional, so we just set up a proportion equation, cross multiply and solve for the unknown:

 

Tree's Height (ft)         Tree's Shadow (ft)

—————————    =  ———————————

Statue's Height (ft)       Statue's Shadow (ft)

 

or,

 

T / 34 cm = 1,600 cm / 96 cm. We need to solve for T (the tree's height). Cross multiply, so that we have:

 

34 * 1,600 = T * 96 ...

 

54,400  = 96T ... now divide each side by 96 to solve for T.

 

54,400/96 = 566 2/3 or 566.67 ft, rounded to the nearest hundredth.