Benji is 55 ft from the base of his apartment building in New York when he spots his friend, Ronny, in the apartment building 150 feet up on the 15th floor. From where he is standing, what is the angle of elevation when he looks up at Ronny? Round to the nearest hundredth.
tan Ø = 150/55 = ...
Ø = ....
Use your calculator to find Ø
make sure it is set to D
enter:
2ndF
tan
(
150
÷
55
)
=
to get 69.86...°
To find the angle of elevation when Benji looks up at Ronny, we can use trigonometry. Specifically, we'll use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.
In this case, the opposite side is the height of the building (150 ft), and the adjacent side is the distance between Benji and the base of the building (55 ft).
So, the tangent of the angle of elevation (θ) is given by the formula:
tan(θ) = opposite/adjacent
Plugging in the values we know:
tan(θ) = 150/55
To find the angle itself, we need to take the inverse tangent (arctan) of both sides. This can also be written as tan^(-1) or atan.
θ = tan^(-1)(150/55)
Using a calculator, we find that θ ≈ 69.09 degrees.
Therefore, the angle of elevation when Benji looks up at Ronny is approximately 69.09 degrees.