Answer:
Distance between cars rounded to the nearest foot is : 1903 ft
Step-by-step explanation:
Notice that two right triangles can be used to represent the diagram of this situation. One between the car whose angle of depression is [tex]28^o[/tex], and the other with the car with angle of depression [tex]35^o[/tex] (see attached image)
Each triangle in the attached image is depicted with a different color. and as one can see, the distance between both cars is the addition of the side "x" in one triangle, to the side "y" in the other.
Notice as well that the information known for both right-angle triangles is one acute angle, and the side opposite to it. And what one needs to find is the side adjacent to this acute angle. Then, the function to use in both triangles, is the tangent:
a) For the [tex]28^o[/tex] [orange] triangle :
[tex]tan(28^o)=\frac{575}{y} \\y=\frac{575}{tan(28^o)} \\y=1081.42\,\,ft[/tex]
b) For the [tex]35^o[/tex] [green] triangle:
[tex]tan(35^o)=\frac{575}{x} \\y=\frac{575}{tan(35^o)} \\y=821.19\,\,ft[/tex]
Therefore the total distance between cars is:
1081.42 ft + 821.19 ft = 1902.61 ft
which to the nearest foot can be rounded as: 1903 ft
Both the cars driven by the motorists on the highway are 1903 feet apart.
Given in the question,
From right triangle ABC,
[tex]\text{tan}(35^\circ)=\frac{AB}{BC}[/tex]
BC = [tex]\frac{AB}{\text{tan}35^\circ}[/tex]
= [tex]\frac{575}{\text{tan}35^\circ}[/tex]
= 821.19 feet
From right triangle ABD,
[tex]\text{tan}(28^\circ)=\frac{AB}{BD}[/tex]
[tex]BD=\frac{575}{\text{tan}28^\circ}[/tex]
= 1081.42 feet
Distance between the cars (CD) = BC + BD
= 821.19 + 1081.42
= 1902.61 feet
≈ 1903 feet
Therefore, distance between the cars is 1903 feet.
Learn more about the angle of elevation and depression here,
https://brainly.com/question/2073490?referrer=searchResults
