Montreal’s Marathon building is 195m tall. From a point level with, and 48m away from, the base of the building, what is the angle of elevation of the top of the building, to the nearest degree?
To find the angle of elevation, we can use the tangent function. The tangent function relates the opposite side, the adjacent side, and the angle of a right triangle.
In this case, the opposite side is the height of the building (195m) and the adjacent side is the distance from the base of the building to the point (48m).
We can solve for the angle of elevation using the formula: tangent(angle) = opposite/adjacent.
tangent(angle) = 195/48
To find the angle, we can take the inverse tangent (or arctangent) of both sides of the equation.
angle = arctan(195/48)
Using a scientific calculator, we can find the arctangent of 195/48, which is approximately 75.4 degrees.
So, the angle of elevation of the top of the building is approximately 75 degrees to the nearest degree.
The height of the building represents
the vertical leg of a rt. triangle, and
the hor dist. from the bottom is the hor. leg of the rt. triangle. The line
of sight from the end of the 48m line
to the top of building is the hyp. The
angle of elevation is the acute angle
between the hyp. and the hor. leg.
TanB = Y/X = 195/48 = 4.06, B = 76.2
deg. = angle of elevation.