Question

Dory's shadow is 1.25m. She stands 4.75m away from the base of the tree, so the tip of her shadow matches the tip of the tree's shadow. Dory is 1.6m tall. How tall is the tree in meters?

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Answer 1

Explanation:

To find the height of the tree, you can set up a proportion based on the similarity of the triangles formed by Dory and her shadow and the tree and its shadow.

Let's use the following variables:

- H = height of the tree (what we want to find)

- D = height of Dory (1.6 meters)

- Sd = length of Dory's shadow (1.25 meters)

- St = length of the tree's shadow (what we want to find)

- Dd = distance of Dory from the base of the tree (4.75 meters)

Now, you can set up a proportion using similar triangles:

(Dory's height / Dory's shadow) = (Tree's height / Tree's shadow)

(1.6 / 1.25) = (H / St)

Now, solve for St:

St = (1.6 / 1.25) * H

To find the length of the tree's shadow (St), you need to know the height of the tree (H). Once you have the value of St, you can calculate the height of the tree (H).

Let's solve for H:

St = (1.6 / 1.25) * H

St = 1.28 * H

Now, you know that St (the length of the tree's shadow) is 4.75 meters because it matches the distance Dory is from the base of the tree.

4.75 = 1.28 * H

Now, solve for H:

H = 4.75 / 1.28

H ≈ 3.71 meters

So, the height of the tree is approximately 3.71 meters.