A tree casts shadow 14 feet long. at the same time, a vertical rod 28 feet high casts a shadow 8 feet long. how tall is the tree

This problem involves using similar triangles because both the tree and the vertical rod are casting shadows at the same time under the same sunlight.

We can set up a proportion using the heights and shadow lengths:

\[
\frac{\text{Height of the tree}}{\text{Shadow of the tree}} = \frac{\text{Height of the rod}}{\text{Shadow of the rod}}
\]

Let \( h \) be the height of the tree, which we are trying to find. Then, the equation is:

\[
\frac{h}{14} = \frac{28}{8}
\]

Now, solve for \( h \):

\[
h = \frac{28}{8} \times 14
\]

Let's calculate the value of \( h \).

The height of the tree is 49 feet.

Would you like more details or have any further questions?

Here are 5 related questions you can try:
1. If the tree's shadow were 20 feet long, how tall would the tree be under the same conditions?
2. If a building casts a shadow 35 feet long, and a 10-foot pole casts a 5-foot shadow at the same time, how tall is the building?
3. What would be the height of a flagpole if it casts a 12-foot shadow, and a 6-foot pole casts a 4-foot shadow at the same time?
4. If the sun's angle changes, causing a tree's shadow to lengthen by 10 feet, how does this affect the height-to-shadow ratio?
5. How can you use trigonometry to determine the height of a tree if the angle of elevation of the sun is known?

**Tip:** When two objects cast shadows under the same sunlight, their height-to-shadow ratios remain the same due to similar triangles.

A tree casts a shadow 14 feet long. At the same time, a vertical rod 28 feet high casts a shadow 8 feet long. How tall is the tree?

Learn how to calculate the height of a tree using similar triangles and proportions. In this problem, a tree casts a 14-foot shadow while a 28-foot rod casts an 8-foot shadow, leading to a simple ratio calculation. Perfect for middle school students studying proportions and geometry.

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