Use the following information to solve the problem. An airport is located at point O. A short-range radar tower is located
at point R. The maximum range at which the radar can detect a plane is 4 miles from point R.
-Assume that R is 2 miles east of O and 7 miles north of O. In other words, R is located at the point (2, 7). An airplane is flying parallel to and 1 miles east of the north axis. (In other words, the plane is flying along the path
X = 1.)What is the greatest distance north of the airport at which the plane can still be detected by the radar
Tower at R? Round your answer to the nearest tenth of a mile.
A)10.9 miles
B)10 miles
C)3)1 miles
D)9)2 miles

Question

Quizplus · Accepted Answer

The radar tower at point R (2, 7) can detect a plane within a 4-mile radius. The plane is flying along the line X = 1, which is 1 mile west of R. To find the greatest distance north of the airport (O) at which the plane can still be detected, we use the Pythagorean theorem. The distance from R to the plane's path is 1 mile (east-west distance), so the north-south distance from R to the edge of the radar's range along the plane's path can be found using the equation: sqrt(4^2 - 1^2) = sqrt(16 - 1) = sqrt(15). The radar tower is already 7 miles north of O, so the total distance north of O at which the plane can be detected is 7 + sqrt(15), which rounds to approximately 10.9 miles.

Use the Following Information to Solve the Problem