Montreal's Marathon building is 395 m tall. From a point level with, and 148m from, the base of the building, what is the angle of elevation to the top of the building?
tanθ = 395/148
To find the angle of elevation to the top of the building, we can use trigonometry. In this case, we can use the tangent function.
First, let's draw a diagram to visualize the situation:
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________ 395m
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P 148m T
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In the diagram, P represents the point from where we are observing the building, T represents the top of the building, and 148m is the distance from P to the base of the building.
Now, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.
The triangle formed by P, T, and the base of the building is a right-angled triangle, where the side opposite to the angle of elevation (θ) is the height of the building (395m) and the side adjacent to θ is the distance from P to the base (148m).
Using the tangent function, we can write:
tan(θ) = opposite / adjacent
tan(θ) = 395m / 148m
Now, we can calculate the angle of elevation:
θ = arctan(395m / 148m)
Using a calculator or an online tool, we find that θ is approximately 69.55 degrees.
Therefore, the angle of elevation to the top of the building from the point 148m away from the base is approximately 69.55 degrees.