Question

A helicopter is flying at an elevation of 575 feet directly above a horizontal highway. Two motorists are driving cars on the highway. The angle of depression to one car is 28° and the angle of depression to the other car is 35°. How far apart are the cars to the nearest foot?

Answer 1

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 $28^o$, and the other with the car with angle of depression $35^o$ (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  $28^o$ [orange] triangle :

$tan(28^o)=\frac{575}{y} \\y=\frac{575}{tan(28^o)} \\y=1081.42\,\,ft$

b) For the $35^o$ [green] triangle:

$tan(35^o)=\frac{575}{x} \\y=\frac{575}{tan(35^o)} \\y=821.19\,\,ft$

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