Cameron is 1.85 meters tall. At 3 p.m., he measures the length of a tree's shadow to be 21.55 meters. He stands 16.6 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.

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29-03-2022
Mathematics

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Cameron is 1.85 meters tall. At 3 p.m., he measures the length of a tree's shadow to be 21.55 meters. He stands 16.6 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.

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vintechnology vintechnology · Answer 1 · 2022-04-04T10:00:22+02:00

The height of the tree can be found by establishing a proportional relationship between the heights and the shadows of the tree and Cameron and the height of the tree to the nearest hundredth of a meter is 2.40 m.

Proportional relationship

Proportional relationships are relationships between two variables where their ratios are equivalent.

Therefore, we will establish a proportion to find the height of the tree.

Cameron height = 1.85 m

Tree shadow = 21.55 m

Cameron shadow length = 16.6 m

height of the tree = x

Therefore,

1.85 / x = 16.6 / 21.55

16.6x = 21.55 × 1.85

x = 39.8675 / 16.6

x = 2.40165662651

x = 2.40 m

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