Question

Christian is 1.35 meters tall. At 10 a.m., he measures the length of a tree's shadow t

be 38.65 meters. He stands 34.4 meters away from the tree, so that the tip of his
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
1.35 m
•34-4 m
•38.65 m


It’s not 1.52

Answer 1

12.28 m

Explanation:

You want the height of a tree that casts a 38.65 m shadow if a 1.35 m person standing 34.4 m from the tree has a shadow with the same tip.

Similar triangles

The ratio of object height to shadow length is the same for both the tree and the person, so we have ...

height/shadow = tree/38.65 = 1.35/(38.65 -34.4)

Then the tree height is ...

tree = 1.35/(38.65 -34.4)·38.65 ≈ 12.28 . . . . meters

The height of the tree is about 12.28 meters.

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