Indirect Measurement Lab Presentation Galileo GanstersPeriod ¾

Goals

• Indirectly measure the height of a tree by

coming up with 3 different methods to do

this.

• This can be done by using the sun, shadows,

proportions, etc.

Designing the Experiment

• The first step was for everyone to put their

heads together and come up with the

procedure.

• After collaborating with each other and

discussing many options, the group came up

with 3 ways to indirectly measure the tree.

Procedure

• Technique 1: Shadows

• First, the group measured the height of a person and

the length of the shadow of a person standing next to a

tree.

• Then, they measured the length of the shadow of the

tree and set up a proportion to find the height of the

tree.

Shadow Technique

=

Pictures From the Experiment

• Left picture: Mercedes measuring the length of tree shadow.

• Right picture: Mike measuring the length of Shelby’s shadow.

Procedure

• Technique 2: Find the Angle

• After using the protractor to calculate the angle

from the ground to the top of the tree, the group

measured the distance between the protractor and

the tree.

• Using the trig function tangent the group found the

height of the tree.

Angle Technique

Protractor

Pictures from Experiment

• Peter using the protractor to measure the angle between the ground and top of tree.

Procedure

• Technique 3: Similar Triangles

• Using similar triangles to compare the height of one

object to another.

• One person holds a piece of string up to cover the tree,

using a protractor the angle between their arms can be

found.

• After measuring the string, distance from the person to

the tree, and height of person from ground to bottom of

arms the height of the tree can be found using

proportions.

Similar Triangles Technique

Bottom arm to ground

Top arm

String

Bottom arm

Total distance

Pictures from Experiment

• Mike is holding

up the string to

block the tree, so

the group can

then take the

measurements.

Results

• Technique 1:

• Height of Person: 5.50 feet

• Shadow of Person: 7.80 feet

• Height of Tree: ?

• Shadow of Tree: 43.00 feet

• After using the proportion method, the height of the tree was found to be 30.3 feet.

Height of person = Height of treeShadow of person Shadow of tree

Results

• Technique 2:

• Angle from ground to top of tree: 51.0

• Distance from protractor to tree: 57.00 feet

• Angle between ground and tree: 90.0

• Height of tree: ?

• After using the trig function tangent, the height of the tree was found to be 70.4 feet.

Tangent = Opposite Tan 51.0˚ = x . Adjacent 57.00 ft

Results

• Technique 3:• Arm length: 27.50 inches

• Angle between arms: 68.0

• Length of string: 10.50 inches

• Distance between person and tree: 57.00 feet

• Height from ground to bottom arm: 5.05 feet

• Height of tree: ?

Results

• Technique 3 (cont.):

length of string = partial height of treearm distance total distance

Partial height of tree + Height from ground to bottom arm = Height of tree

• By using proportions, part of the height of the tree was found, then after adding the height from ground to bottom of arm, the tree was found to be 26.9 feet tall.

Possible Errors

• Surface area outside was not flat

• The tree was not straight

• Protractor was very undersized and therefore inaccurate

Conclusion

• After applying already known mathematical

skills to this real-life situation the height of a

tree was found three different ways

• Some errors were made which made some

results a little off, that is why doing it three

different ways improved accuracy.

Galileo Gangster’s Tree