This is a great math problem, can you solve it?

Question

I had a large tree in the middle of my back yard. I wanted to have it cut down but was afraid it might hit my fence. It was 2pm on a clear sunny day. I need to know how tall the tree was i guess but i cant climb the tree (wheelchair bound). I had only a yard stick, a tape measure, and a pencil and paper. In 5 minutes i knew how tall the tree was. Now, please someone tell me how i did it. It's an east math solution........dang, i hope i didnt leave any info out, this question really helped me to like math and know that you really may use it someday.

Answer 1

yes, just measure the length of the shadow on the ground.
now use pythagoras theorem.

Answer 2

Since it was 2pm on a clear sunny day you can measure the shadow of the yard stick and the shadow of the tree.

Then you can use a proportion to figure out the height of the tree:

height_of_tree / shadow_of_tree = 1 yard / shadow_of_yardstick

Answer 3

I have the strong sucpect that you have read the Wiki How from today :-)

Anyhow:

Shadow Method
Know your exact height in the shoes you will be wearing to perform this method.

Stand next to the tree or the object to be measured. For best results, do this method on a bright, sunny day. If the sky is overcast, it may be difficult to tell exactly where the shadow’s tip is

Measure the length of your shadow. Use a tape measure or yardstick to measure your shadow from your feet to the tip of your shadow. If you don’t have someone to assist you, you can mark the end of the shadow by tossing a rock onto it while you’re standing. Or better yet, place the rock anywhere on the ground, and then position yourself so the tip of your shadow is at the rock; then measure from where you're standing to the rock.
Measure the length of the tree’s shadow. Use your measuring tape to determine the length of the tree’s shadow from the base of the tree to the tip of the shadow. This works best if the ground all along the shadow is fairly level; if the tree is on a slope, for example, your measurement won’t be very accurate. You want to do this as quickly as possible after measuring your shadow, since the sun’s position in the sky (and hence the shadow length) is slowly but constantly changing. If you have an assistant you can hold one end of the measuring tape while he or she measures the tree’s shadow, and then you can immediately measure your shadow.

Calculate the tree’s height by using the proportion of your shadow’s length to your height. Since you know the length of the tree’s shadow, and you also know that a certain height (your height) produces a certain shadow length (the length of your shadow), you can determine the tree’s height with a little math. Multiply the length of the tree’s shadow by your height, and then divide the resulting number by the length of your shadow. For example, if you are 5 feet tall, your shadow is 8 feet long, and the tree’s shadow is 100 feet long, the height of the tree is (100 x 5) / 8 = 62.5 feet. Note that the order of your multiplication does not matter.


OR:

A distant view Stand far enough from the tree so you can view the whole tree—top to bottom—without moving your head. For the most accurate measurement, you should stand so that you are on a piece of ground that is about level with the ground at the tree’s base. Your view of the tree should be as unobstructed as possible.

Have a friend stand near the tree.

Hold a pencil or a small, straight stick (such as a paint stick or ruler) in one hand and stretch your arm out so that the pencil is at arm’s length in front of you (between you and the tree).

Close one eye and adjust the pencil up or down so that you can sight the very top of the tree at the top of the pencil. This is easiest if you turn the pencil so that the sharpened point is pointing straight up. The tip of the pencil should thus just cover the top of the tree in your line of sight as you look at the tree “through” the pencil.

Move your thumb up or down the pencil so that the tip of your thumbnail is aligned with the tree’s base. While holding the pencil in position so that the tip is aligned with the tree’s top (as in step 3), move your thumb to the point on the pencil that covers the point (again, as you look “through” the pencil with one eye) where the tree meets the ground.

Rotate your arm so that the pencil is horizontal (parallel to the ground). Keep your arm held straight out, and make sure your thumbnail is still aligned with the tree’s base.

Have your friend move so that you can sight his or her feet “through” the point of your pencil. That is, your friend’s feet should be aligned with the pencil’s tip. He or she may need to move backward, sideways, or diagonally. Since, depending on the height of the tree, you may need to be some distance away from your friend, consider using hand signals (with the hand that is not holding the pencil) to tell him or her to go farther, come closer, or move to the left or right.

Measure the distance between your friend and the tree. Have your friend remain in the place or mark the spot with a stick or rock. Then use a measuring tape to measure the straight-line distance between that spot and the base of the tree. If you don’t have a measuring tape you can pace out the distance, although this will not be as accurate. The distance between your friend and the tree is the height of the tree.

Answer 4

Stick the yard stick in the ground and measure the shadow.
Measure the tree's shadow and compare

Answer 5

Measure the tree's shadow.
place the yardstick at the same angle as the tree & measure it's shadow. (reference ratio)

Do a little similar sides of similar triangles are similar by proportion, and assuming the tree's topmost shadow point isn't occluded by the branches' spread...you got it!

Answer 6

you used the shadow of the tree. casted by the sun..
and you got two of the sides of the triangle
the tree formed. then you used the pathagorem therom
to find how tall the tree was?

Answer 7

you used the tree's shadow

Answer 8

You measured its shadow.

Answer 9

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.................................................................got it