Question

Maya is 1.65 meters tall. At 12 noon, she measures the length of a tree's shadow to be 21.15 meters. She stands 16 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Answer 1

Assuming Maya is 1.65 meters tall and  measures the length of a tree's shadow to be 21.15 meters the height of the tree to the nearest hundredth of a meter is 6.78m

First step

tan=h/(21.15-16)=1.65/(21.15-16)

tan=h/5.15=1.65/5.15

1.65/5.15=h/5.15

Now let find the height of the tree

h=21.15×1.65/5.15

h=34.8975/5.15

h=6.776

h=6.78m (Approximately)

Inconclusion Assuming Maya is 1.65 meters tall and  measures the length of a tree's shadow to be 21.15 meters the height of the tree to the nearest hundredth of a meter is 6.78m.

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