LAB measurement
To investigate ratios
How to find the height of a tree.
source: wikihow, to know how ..
INTRODUCTION - fill the blank for full credit
See the illustration below ? The 2 triangles have the same shape but not the same size.
The angles are the same. You can place the small triangle in the large triangle as shown in the
2nd image.
their sides are proportional. This means that every side of one triangle will be in a fixed ratio with the corresponding side of the other triangle.
a/b = d/e or a/d = b/ e
PROCEDURE
PART1: Find the height of a tree using its shadow and yours
You are going to measure the shadow of a tree and the shadow of a person.
Step1: With your team, get some tapes, meter stick, string, chalk, the lab. Go outside on a Sunny day.
Step2: Find a pole or a tree on a flat ground with a nice , visible shadow. You have to be quick because the Sun moves. Decide who will measure distances, who will collect the data in the tABLE and who will have her/his shadow recorded.
step3: Measure the length of the tree's shadow. You can use the string. (Someone hold the string at the base of the tree to the tip of the shadow). Then use your meter stick to find the length.
Units are in meters. Record in the TABLE
step4: Quick. Measure the the length of the person shadow.
| shadow2= shadow of the tree (meters) | shadow1 = shadow of the person (meters) | H = height of the person (meters) | X = height of the tree (meters) X= (shadow2/shadow1) x H |
step5: Back in the lab find the height of the person. She or he should stay against a wall. Record in the TABLE.
ANALYSIS
Find the height of the tree using similar triangles 's rule. Use the image below to help you.
shadow2/shadow1 = X/H
(same ratios between the sides of the similar triangles )
Plug the numbers into the equation and solve for X. X = ______________
hint: cross multiply.
shadow2 x H = shadow 1 x X
X= (shadow2/shadow1) x H
Does this number makes sense ?
PART2: This method uses a pencil and at least 3 persons. One person to use the pencil,
one person to stand near the tree and one person to measure the distance tree/standing person.
1) Use the same tree. From a distance hold a pencil with your thumb. Cover the tree with your pencil such as the base of the tree is at your thumb level and the tip of the pencil matches the tip of the tree. You need to move the thumb up or down. 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.
2) Ask you friend to stay near the tree. 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.
3) 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.
4) Have the third person find the distance tree-standing person. THis is the height of your tree !
Math is amazing ! and so is Physics !
H = ____________
ANALYSIS
1) Do you get the same result as in PArt 1? Which method seems the most accurate ?
the easiest ? why ?
GOING FURTHER try without hints first. Help each other. Discuss. work the problems out.
The tips of the tree's shadow and of Susie shadow match. Find the height of the tree.
