Measuring Inaccessible Heights
Overview
Without mathematics, it is nearly impossible to measure the height of large objects like the pyramids,
parliament buildings or large radio towers. Using trigonometry, you can calculate the height of really
tall objects while remaining on the ground. Even the distance to the moon and stars can be calculated
using trigonometry. There are many tools to help measure large distances. You will initially use a Clinometer to help measure the angles needed to calculate different heights, and then use methods that
require very little tools at all.
Method/Project
1. Building a Clinometer
You will need:
 protractor
 piece of string (about 15 cm) & tape
 half a straw
 small weight (i.e. paper clips)
 measuring tape or metre stick
(There are many different types of Clinometers)
How to make a Clinometer:
1. Attach an end of the string to the center of the protractor and tie the weight to the other end. The
string needs to hang exactly from the “T” of the protractor made by the 90 line.
2. Tape the straw to the protractor so it crosses the center and the 90 mark.
3. Ensure that you can clearly see through the straw; the weight must provide tension on the string.
Using a Clinometer:
1. Hold the protractor with the straight edge
on top and the weight hanging down.
2. Look through the straw and find the object
you want to measure. Make sure you are
looking right at the top of the object
3. Have a partner record the acute (less than
90) angle measurement where the thread
lies against the protractor.
4. Using the measuring tape, measure
a) how far it is from the ground to where
the centre of the protractor was when
you measured the angle (place where
string is attached)
b) The distance from you to the object.
2. Finding the height of the Flag Pole:
A) You will need the following measurements:
1) Distance from person to flag pole (length 'd')
d = _____________ metres
2) Distance from ground to Clinometer (length 'h')
h = _____________ metres
3) Angle measured using Clinometer (Angle 'A')
A = _____________ degrees
4) Calculate Angle 'B' (A + B = 900)
 B = 900 - _______0 = _______0
B) Calculating the Height Using Trigonometry Ratios
1) Notice that the lengths 'd' and 'y' are the same. Write them onto your diagram, along with B
2) Calculate the height of 'x' in metres. Circle the trigonometry ratio you will use.
3) The total height of the flagpole is h + x = _______m. + _______m. = _______m.
4) Does your answer make sense? Why or Why not?
sinA =
opp
hyp
cosA =
adj
hyp
tanA =
opp
adj
3. Finding the height of other inaccessible objects.
Complete this section on separate paper, and include appropriate diagrams and calculations.
A) Find the height of another tall object around the school grounds (building, tree, etc.)
B) Find the height of a unique inaccessible object, using your clinometer. Examples could include the
CN Tower, a large office building, a tall white pine tree, a T.V./radio tower, etc.
For both inaccessible objects,
 Draw a diagram to help you calculate the height of the object.
 Using the Clinometer and measuring tape, record the necessary measurements to find the height of
the objects. The process and calculations will be similar to the flag pole problem.
 Prepare a brief report, showing all calculations and diagrams, to explain how you determined the
height of both objects.
 List any possible sources of error may have occurred in your investigation of the object’s height.
Evaluation
Name: ____________________________
1. Calculations for finding the height of the flag pole. ______/10: Knowledge.
2. Calculations and method for finding the height of two other inaccessible objects. ______/10: App.
3. Designing your own clinometer:
Criteria
Level 1
Level 2
Level 3
Level 4
Understanding core
concepts of clinometer’s accuracy and
effectiveness Thinking/Inquiry.
Demonstrates limited understanding of
concepts
Demonstrates some
understanding of
concepts
Demonstrates considerable
understanding of
concepts
Demonstrates thorough understanding
of concepts
Crafts a professional
clinometer, that makes
effective use of design
and appropriate material choice
Demonstrates limited crafting ability,
and selects only
familiar materials
Demonstrates crafting ability, and
provides some diversity in material
selection
Demonstrates complex crafting ability,
and uses familiar and
unfamiliar material
selection
Uses novel opportunities in
demonstrating crafting ability and
selects the most
appropriate materials
Application
Evaluation
Name: ____________________________
1. Calculations for finding the height of the flag pole. ______/10: Knowledge.
2. Calculations and method for finding the height of two other inaccessible objects. ______/10: App.
3. Designing your own clinometer:
Criteria
Level 1
Level 2
Level 3
Level 4
Understanding core
concepts of clinometer’s accuracy and
effectiveness Thinking/Inquiry.
Demonstrates limited understanding of
concepts
Demonstrates some
understanding of
concepts
Demonstrates considerable
understanding of
concepts
Demonstrates thorough understanding
of concepts
Crafts a professional
clinometer, that makes
effective use of design
and appropriate material choice
Demonstrates limited crafting ability,
and selects only
familiar materials
Demonstrates crafting ability, and
provides some diversity in material
selection
Demonstrates complex crafting ability,
and uses familiar and
unfamiliar material
selection
Uses novel opportunities in
demonstrating crafting ability and
selects the most
appropriate materials
Application
Measuring Inaccessible Heights
Evaluation
1. Calculations for finding the height of the flag pole. ______/10: Knowledge.
2. Calculations and method for finding the height of two other inaccessible objects. ______/10: App.
3. Designing your own clinometer:
Criteria
Level 1
Understanding core Demonstrates limconcepts of clinome- ited understanding
of concepts
ter’s accuracy and
effectiveness Thinking/Inquiry.
Crafts a professional
clinometer, that
makes effective use
of design and appropriate material
choice
Application
Demonstrates limited crafting ability,
and selects only
familiar materials
Level 2
Level 3
Demonstrates some Demonstrates conunderstanding of
siderable
concepts
understanding of
concepts
Level 4
Demonstrates thorough understanding
of concepts
Demonstrates crafting ability, and
provides some diversity in material
selection
Uses novel opportunities in
demonstrating
crafting ability and
selects the most appropriate materials
Demonstrates complex crafting
ability, and uses
familiar and unfamiliar material
selection
PROJECT EXTENSIONS OR ALTERNATIVES: Finding the height of Inaccessible objects using
 Similar Triangles
 Mirror Method