A popular tourist attraction in Ottawa is the Peace Tower which rises from the Centre Block of the Parliament Buildings. Describe at least one method that you could use to estimate the height of the tower, including the measurements you would need to make. Hint: Include labelled diagram, explanation of similar triangles, and the proportion you would use.
Your help is greatly appreciated.
Thank you for your time.
I will be happy to critique your thinking on this.
To estimate the height of the Peace Tower, we can use the concept of similar triangles along with some simple measurements. Here's a step-by-step description of one method:
1. Find a suitable location to estimate the height of the Peace Tower. Ideally, this spot should have a clear view of the tower and should be at a distance where it can be easily measured.
2. Measure the horizontal distance from your location to a point directly in line with the base of the Peace Tower. You can either use a measuring tape or rely on satellite imagery tools such as Google Maps to get this measurement (let's call it A).
3. Now, find a vertical object close to your location (like a lamppost, tree, or any other reasonably straight object) and measure its height (let's call it B). Make sure to take this measurement from the base to the top of the object.
4. Stand at your chosen location and take a sighting device (such as a rangefinder or a smartphone that can measure angles).
5. Align your sighting device with the top of the identified vertical object (B). Measure the angle between the horizontal line of sight and the vertical line leading to the top of the object (let's call it C).
6. Move your sighting device to align with the top point of the Peace Tower, keeping the same angle of elevation (C) as measured previously.
7. Now, measure the horizontal distance from your location to the base of the Peace Tower using your sighting device. Let's call this distance D.
8. Construct a diagram to illustrate the measurements and angles as described above to visualize the process.
----> D
/ \
/ \
A B
| /
| /
|/
9. Now, we can establish a proportion using the concept of similar triangles. By comparing the two sets of triangles formed by points A, B, and C, we have the following proportion:
D/A = B/ (B + h)
Where h represents the height of the Peace Tower that we want to estimate.
10. To determine the height of the Peace Tower (h), rearrange the equation as follows:
h = D*B / A - B
11. Plug in the values of the measurements you made to calculate the estimated height of the Peace Tower.
Remember that this method is an estimation and may not be entirely accurate. It relies on the assumption that the vertical object (B) and the Peace Tower are perfectly straight, which may not be the case. Nonetheless, it should provide you with a reasonable approximation of the tower's height.