a popular tourist attraction in ottawa is the Peace tower, which rises from the Center Block of the Parliment buildings. Describe at least one method that you could use to estimate the height of the tower, including the measurments you would need to make. Include labelled diagram, explination of similar triangles, and the proportion you would use
find (or set up) a small pole. Measure its height and the length of its shadow. Figure the ratio of height to width.
Measure the shadow of the tower, and use the same ratio to figure its height.
Note: Don't try this near noon! Why not?
To estimate the height of the Peace Tower in Ottawa, you can use a method called "similar triangles." This involves comparing the ratios of corresponding sides of two similar triangles. Here is how you can approach this estimation:
1. Select a reference point: Find a spot where you have a clear view of the Peace Tower. This point should be far enough from the tower so that you can measure the angle of elevation accurately.
2. Measure the distance: Use a measuring tape or other measuring tools to determine the distance from your reference point to the base of the Peace Tower. Let's call this distance "d1."
3. Measure the angle of elevation: Using a clinometer or a smartphone app with an inclinometer feature, measure the angle of elevation from your reference point to the top of the Peace Tower. Let's call this angle "θ."
4. Draw a diagram: Create a labeled diagram to help visualize the triangles involved in this estimation. Label the distance from the reference point to the base of the tower as "d1" and the height of the tower as "h." Also, label the angle of elevation as "θ."
5. Identify the similar triangles: In the diagram, you have a larger triangle formed by your reference point, the base, and the top of the tower (let's call this larger triangle ABC). You can identify a smaller similar triangle formed by the reference point, the base, and a point on the tower at a height "h" (let's call this smaller triangle ADE). The angle at the top of the tower in both triangles will be the same, given by θ.
6. Set up the proportion: The corresponding sides of similar triangles are proportional. In this case, AB is corresponding to AD, and AC is corresponding to AE. Therefore, you can set up the proportion as follows:
AB/AC = AD/AE
Since both triangles share the same angle θ, the ratio AB/AC can be represented as:
AB/AC = tan(θ)
7. Solve the proportion: Substitute the known values into the proportion and solve for h:
tan(θ) = AD/AE
tan(θ) = d1/h
Rearrange the equation to solve for h:
h = d1 / tan(θ)
8. Calculate the height: Plug in the measured values of d1 and θ into the equation from Step 7 to find the estimated height of the Peace Tower.
By using the method of similar triangles and the measurements of distance and angle of elevation, you can estimate the height of the Peace Tower in Ottawa.