Answer:
7086.9 feet.
Step-by-step explanation:
We can see that the two triangles formed by the plane and the cars are similar, because they share a common angle (90 degrees) and have corresponding angles that are equal (the angles of depression). Therefore, we can use the proportionality of corresponding sides to find the distance between the cars. Let x be the distance from the plane to the car with 35 degrees angle of depression, and y be the distance from the plane to the car with 52 degrees angle of depression. Then we have:
- x / sin(35) = y / sin(52) = 5150 / sin(90)
- Cross-multiplying and solving for x and y, we get:
- x = 5150 x sin(35) / sin(90) x = 2957.8 feet
- y = 5150 x sin(52) / sin(90) y = 4129.1 feet
- The distance between the cars is the sum of x and y:
- d = x + y d = 2957.8 + 4129.1 d = 7086.9 feet
The answer is 7086.9 feet.