Question

1. vicky needs to know the height of a tree in her yards without climbing it. she goes outside when the sun is low and measures the length of the trees shadow to be 24 feet long. at the same time, she measures her own shadow to be 8 feet long. calculate the height of the tree given that vicky is 5 feet tall.

Explanation:

Identify the given values and variables

Using the Similar Triangles Application knowledge point
Let \(H\) be the height of the tree in feet.

• Height of Vicky: \(h = 5\text{ ft}\)
• Length of Vicky's shadow: \(s = 8\text{ ft}\)
• Length of the tree's shadow: \(S = 24\text{ ft}\)

Set up the similarity proportion

Using the Triangle Similarity knowledge point

$$ \frac{H}{S} = \frac{h}{s} $$

Substitute the values and solve for H

Using the Similar Triangles Application knowledge point

$$
LATEXBLOCK0
$$

Answer:

15 feet