Answer :
Answer:
The distance between two cars is 110.64 feet.
Step-by-step explanation:
Angle of depression is defined as an angle between the line of sight and the horizontal.
Remember in a right angled triangle, the angle of depression is always same as the angle of elevation.
If [tex]\theta[/tex] be the angle of depression then,
[tex]tan\theta=\frac{opposite}{adjacent}[/tex]
Given that,
Two car are travelling toward a hotel on the same road.
The height of the given building is 600 feet.
For the first car:
The angle of depression = The angle of elevation = 52°
Let the horizontal distance between the building and the car be x.
Here, [tex]\theta =52 ^\circ[/tex], opposite = 600 feet, adjacent = x
[tex]tan 52^\circ=\frac{600}{x}[/tex]
[tex]\Rightarrow x=\frac{600}{tan 52^\circ}[/tex]
[tex]\Rightarrow x\approx 468.77[/tex] feet
For the second car:
The angle of depression = The angle of elevation = 46°
Let the horizontal distance between the building and the car be y.
Here, [tex]\theta =46 ^\circ[/tex], opposite = 600 feet, adjacent = y
[tex]tan 46^\circ=\frac{600}{y}[/tex]
[tex]\Rightarrow y=\frac{600}{tan 46^\circ}[/tex]
[tex]\Rightarrow x\approx 579.41[/tex] feet
The distance between two cars is
= The distance of the second car from the building - The distance of the first car from the building
=(579.41-468.77) feet
=110.64 feet.