Measuring Height Indirectly

Purpose:

To use methods of Trigonometry and Pythagorean's Theorem to measure the height of a person.
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Introduction:

When a triangle has 90o as one of its angles, there are several trigonometric rules that can be used to analyze it.
As a general practice, the side that is directly across from the right angle is called the hypotenuse.
Using another angle as a reference, thetaWordScreenSnapz002.jpgfor example, the side that right next to thetaWordScreenSnapz002.jpgis called the adjacent while the remaining angle is the opposite.
Trigonometry offers three basic identities for this triangle:


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These identities are commonly referred to as "SOH", "CAH", and "TOA".
In addition to trigonometry, Pythagorean's Theorem, c2 = a2 + b2, can also be applied to a right triangle.


Instructions

  1. Each person in your lab group must read every page in this online procedure. Along the way, there will be questions that you must answer.
  2. Designate one person in your group as the Data Recorder. This person should open the Google document Experiment 2 - Measuring Height Indirectly for the approved answer template.
  3. When this Google document opens, sign in to your Google account.
  4. From theFILE Menu, chooseMake a copy...
  5. From theFILE Menu, chooseRename...and rename the document as follows: Exp 2 - Period (1, 3, 6, or 8) - Group #.
  6. Share this document with the members of your group and with Mr. Skubis at HSTScience@gmail.com.
  7. As a group, answer all questions. Remember to use complete sentences and be mindful of grammar, spelling, and punctuation.
  8. As an individual, you will complete Calculation Requirements as specified below.
  9. Finally, AS A GROUP write a CONCLUSION as described at the end of this lab. Submit the conclusion on the Google document for full credit.
  10. REMEMBER: **Plagiarism** is a form of **Academic Dishonesty** which carries harsh consequences. DO YOUR OWN WORK!



Procedure

Consider the 2nd man from the photograph above. Construct a right triangle around him so that his height (H) is opposite theta. You will be verifying this value mathematically with the measurements made in this experiment.
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  1. Obtain a piece of string from your instructor. Make sure there are small knots at each end. Measure the length of the string from knot-to-knot to the nearest 0.1 centimeter with a meter stick. This string is the hypotenuse of the triangle as indicated by the letter "L" above. Record this measurement.
  2. Hold one end of the string on the top of your head. Have your partner extend the string to the floor in front of you.
  3. Hold the string taut and without moving measure the distance along the floor (F) from where the outstretched knot touches the ground to an imaginary mid-line extending down through your head to your feet. This side is adjacent to the angle WordScreenSnapz002.jpg. Again measure to the nearest 0.1 centimeter. Record this measurement.
  4. Again with the string taut and without moving, measure and record the angle the string makes with the floor. This is WordScreenSnapz002.jpg as indicated above.
  5. Measure your ACTUAL HEIGHT to the nearest 0.1 centimeter by standing against the wall.
  6. Repeat this process for every member of your group.



Calculation Requirements

As an individual, prepare a handwritten document that shows ALL calculations that pertain to YOUR DATA in this experiment. This document must be neatly written on looseleaf paper or word-processed. NO FRAYED EDGES. For this experiment, that means you need to show the 5 calculations including each relative error necessary to complete the Calculations Table on the Google Doc.

You should follow the format: ANALYZE, PLAN, COMPUTE, EVALUATE.

In the PLAN stage, be sure you show all the Algebra involved with solving the problems.

In the COMPUTE stage, include the actual experimental data with their proper SI units and show how they plug into the equation. Be sure your answer has 3 sig figs and proper SI units (if applicable).


Analysis

Calculate your Indirect Height by using the only the data specified in each step below.
  1. Use WordScreenSnapz002.jpg and the length of string (L).
  2. Use WordScreenSnapz002.jpg and the distance along the floor (F).
  3. Calculate a NEW value for WordScreenSnapz002.jpg by using (L) and (F).
  4. Use the NEW WordScreenSnapz002.jpg and (F) to calculate your Indirect Height.
  5. Use the Pythagorean Theorem.
  6. On the Google Document, indicate the equation used for each calculation above.
  7. Using the height you measured against the wall as your ACTUAL HEIGHT, calculate the % Relative Error (ER) in your answers for methods 1-3 & 5 above.
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where ER is the % Relative Error, Observed is your calculated height for each method, and Actual is your height measured against the wall.