Question

Ellie is 1.75 meters tall. At 3 p.m., she measures the length of a tree's shadow to be 20.25 meters. She stands 16.2 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

Answer: the height of the tree is 20.25 meters to the nearest hundredth of a meter.

Explanation:

Answer 2

To find the height of the tree, we can use the tangent of the angle between the top of the tree and the tip of Ellie's shadow to find the height of the tree.

Tangent(theta) = Opposite / Adjacent

Opposite = height of tree

Adjacent = distance between Ellie and the tree

Tangent(theta) = height of tree / 16.2

We know that:

Tangent(theta) = 20.25 / 16.2

We can solve for the height of the tree by multiplying both sides of the equation by 16.2:

height of tree = Tangent(theta) * 16.2

height of tree = (20.25 / 16.2) * 16.2height of tree = 20.25

So, the height of the tree is 20.25 meters to the nearest hundredth of a meter.