Indirect Measurement Lab Presentation Galileo Gansters Period 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: feet After using the proportion method, the height of the tree was found to be 30.3 feet. Height of person =Height of tree Shadow of person Shadow of tree

Results Technique 2: Angle from ground to top of tree: 51.0  Distance from protractor to tree: 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 ft

Results Technique 3: Arm length: inches Angle between arms: 68.0  Length of string: inches Distance between person and tree: feet Height from ground to bottom arm: 5.05 feet Height of tree: ?

Results Technique 3 (cont.): length of string = partial height of tree arm distancetotal 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