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QuestionA tree's shadow is 24 ft, and a 4-ft post casts a 6-ft shadow. What is the height of the tree?

Studdy Solution

STEP 1

Assumptions1. The tree and the post are both vertical and cast shadows along the ground. . The lengths of the shadows are proportional to the heights of the objects casting them.
3. The shadow of the tree is24 ft long.
4. The shadow of the4-ft post is6 ft long.

STEP 2

We can set up a proportion to find the height of the tree. The proportion is set up as followsHeight of treeShadow of tree=Height of postShadow of post\frac{Height\, of\, tree}{Shadow\, of\, tree} = \frac{Height\, of\, post}{Shadow\, of\, post}

STEP 3

Now, plug in the given values for the height of the post, the shadow of the post, and the shadow of the tree.
Height of tree24 ft= ft6 ft\frac{Height\, of\, tree}{24\, ft} = \frac{\, ft}{6\, ft}

STEP 4

To solve for the height of the tree, we can cross-multiply.
Height of tree=24 ft×4 ft6 ftHeight\, of\, tree = \frac{24\, ft \times4\, ft}{6\, ft}

STEP 5

Calculate the height of the tree.
Height of tree=24 ft×4 ft ft=16 ftHeight\, of\, tree = \frac{24\, ft \times4\, ft}{\, ft} =16\, ftThe height of the tree is16 feet.

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