Answer:
0.4476 degrees.
Step-by-step explanation:
Let θ be the angle between the beam and the road. The given values form a right triangle with the distance that the beam drops ( h=3 in) being the side opposite to θ and the distance in front of the car (x=32 ft or x=384 in) being the side adjacent to θ.
Therefore, θ is given by:
[tex]tan^{-1}(\theta) = \frac{h}{x}\\tan^{-1}(\theta) = \frac{3}{384}\\ tan^{-1}(\theta) = \frac{1}{128}\\\theta=0.4476^o[/tex]
The angle between the beam and the road is 0.4476 degrees.
Using the tangent, it is found that the angle between the beam and the road in degrees is of 359.55.
The tangent of an angle [tex]\alpha[/tex] is given by vertical change divided by the horizontal change, that is:
[tex]\tan{\alpha} = \frac{\Delta_y}{\Delta_x}[/tex]
In this problem, the beam drops 3 in for each 32 ft in front of the car, hence [tex]\Delta_y = -3, \Delta_x = 32(12) = 384[/tex]
Then:
[tex]\tan{\alpha} = \frac{-3}{384}[/tex]
[tex]\alpha = \tan^{-1}{\left(\frac{-3}{384}\right)}[/tex]
Using a calculator:
[tex]\alpha = 359.55[/tex]
The angle is of 359.55º.
A similar problem is given at https://brainly.com/question/24278338
