Where in your city or region can you see the farthest? The higher up you are, either in a building or on top of a hill (or a building on a hill), the farther you will be able to see. If there are no obstructions, you can see all the way to the horizon. With the Pythagorean Theorem and the radius of the Earth (r = 6,371 km), a few calculations can reveal the distance to the horizon (d) for any height (h). Given the height of my eye above the floor, 174 cm, if I stand on the beach and look out over the ocean to the horizon, I should be able to see about 4.708 km. A recent podcast from "A Problem Squared" (episode 022) featured a similar question. The question that was submitted by a listener asked, "What's the furthest away you can see something from earth, that is also on the earth?" This question made me think about a new building being built near where I live in Halifax. Richmond Yards, at a height of 103.3 m, it will be the tallest in Atlantic Canada when it is completed. It is also built one of the highest parts of the Halifax Peninsula at 60 metres above sea level. I wonder if the view from the top of this new building will be the longest view in Halifax? Or could it even be the longest line of sight in the province of Nova Scotia? So if I stand at the top of the Richmond Yards tower (103.3 m), located on a hill that is 60 m above sea level, how far should I be able to see if there are no obstructions? Using the formula above, my new height would be 103.3 m + 60 m + 1.74 m = 165.04 m. Given that height, the distance to the horizon would be 45.858 km. That is quite an improvement. Do you think there is a spot in your town or region where you could see farther? Where in Nova Scotia can you look the furthest away at something else, that is also in Nova Scotia? Do you know where the highest point in Nova Scotia is? What about in furthest view in all of Canada? From the top of the CN Tower? From the top of Mount Logan, the tallest mountain in Canada with a summit of 5,959 m? What other factors effect how far you can see? What about seeing past the horizon to a tall building or mountain that sticks up over the other side of the horizon? NS Outcomes: Mathematics 8 - M01 Students will be expected to develop and apply the Pythagorean theorem to solve problems. Mathematics 9 - M01 Students will be expected to solve problems and justify the solution strategy, using the following circle properties: [...] A tangent to a circle is perpendicular to the radius at the point of tangency. EL
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