Answer:
the angle of elevation is 12.56°
Step-by-step explanation:
the height of the ramp represents the opposite side and the length of the ramp the hypotenuse
we see that it has (angle, hypotenuse, opposite)
well to start we have to know the relationship between angles, legs and the hypotenuse
a: adjacent
o: opposite
h: hypotenuse
sin α = o/h
cos α= a/h
tan α = o/a
we choose the one with opposite and hypotenuse
sin α = o/h
sin α = 5ft / 23ft
sin α = 5/23
α = sin^-1 ( 5/23)
α = 12.56°
the angle of elevation is 12.56°
The angle of elevation of the 23-foot ramp, to the nearest tenth of a degree, if its final height is 5 feet is 12.6°.
The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
[tex]\rm Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
We know that the length(Hypotenuse) of the ramp is 23 feet, while the height(Perpendicular) of the ramp is 5 feet. Thus, using the Sine function of the trigonometry can be written as,
[tex]\rm Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}\\\\Sin(\theta) = \dfrac{5}{23}\\\\\rm (\theta) = Sin^{-1}\ \dfrac{5}{23}\\\\\theta = 12.555^o \approx 12.6^o[/tex]
Hence, the angle of elevation of the 23-foot ramp, to the nearest tenth of a degree, if its final height is 5 feet is 12.6°.
Learn more about Sine:
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