Shadow Lengths: Friend vs Tree

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In summary, the tree is 8 feet tall and the person is 5 feet tall. The shadow of the person is 8 feet long and the shadow of the tree is 28 feet long.
  • #1
Abdullah Qureshi
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At certain time of day, the shadow of your friend who is 5 ft tall measures 8 ft. At

the same time, the shadow of a tree measures 28 ft. Draw a diagram to represent

the situation. How tall is the tree?
 
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  • #2
Beer soaked request follows.
Abdullah Qureshi said:
At certain time of day, the shadow of your friend who is 5 ft tall measures 8 ft. At

the same time, the shadow of a tree measures 28 ft. Draw a diagram to represent

the situation. How tall is the tree?
Please show us what you have tried and exactly where you are stuck.

We can't help you if we don't where you are stuck.
 
  • #3
jonah said:
Beer soaked request follows.

Please show us what you have tried and exactly where you are stuck.

We can't help you if we don't where you are stuck.
how to draw it and put the numbers
 
  • #4
Beer soaked query follows.
Abdullah Qureshi said:
how to draw it and put the numbers
What did you use to type your problem?
 
  • #5
The person and the tree are, I assume, standing upright. Draw one horizontal line representing the ground, a vertical line on that horizontal line representing the person, and a longer vertical line representing the tree. Did you really need to be told that?

Now draw lines from the top of each vertical line to the "ground", at the SAME ANGLE. That is the important part. That represents the sun's rays and the sun is at the same angle for person and tree. The distance from each vertical line to the the point where the "sun's rays" meet the "ground" is the length of the shadow.

Now, do you see that you have two "similar triangles"? What do you know about similar triangles?

(If you want to do well in mathematics you are going to have to have a lot more imagination than you have shown here!)
 

FAQ: Shadow Lengths: Friend vs Tree

1. What is the relationship between the shadow length of a friend and a tree?

The shadow length of a friend and a tree is determined by the angle of the sun's rays and the distance between the object and the surface where the shadow is cast. The closer an object is to the surface, the longer the shadow will be. Therefore, if the friend and tree are at the same distance from the surface, their shadow lengths will be the same.

2. Why do shadows change in length throughout the day?

Shadows change in length throughout the day because the angle of the sun's rays changes as it moves across the sky. When the sun is directly overhead, shadows are shorter because the light is hitting objects at a more perpendicular angle. As the sun moves lower in the sky, the angle of the light changes, causing shadows to become longer.

3. How does the height of an object affect its shadow length?

The height of an object does not directly affect its shadow length. The angle of the sun's rays and the distance between the object and the surface where the shadow is cast are the main factors that determine shadow length. However, taller objects may appear to have longer shadows because they are casting their shadows over a larger surface area.

4. Can the shadow length of an object be longer than the object itself?

Yes, the shadow length of an object can be longer than the object itself. This is because the angle of the sun's rays and the distance between the object and the surface where the shadow is cast can create a longer shadow. This is often seen with tall buildings or trees.

5. How can I calculate the shadow length of an object?

To calculate the shadow length of an object, you will need to know the angle of the sun's rays and the distance between the object and the surface where the shadow is cast. You can then use trigonometry to calculate the length of the shadow. Alternatively, you can measure the length of the shadow and the height of the object and use simple math to determine the ratio between the two.

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