+185 An airplane is 115 miles due east of radio station A. A second radio station is 136 miles due north of A. What are the distance and bearing of the second radio station from the airplane?
+36919 To find the ANGLE from the airplane to the second radio station:
tan x = 136/115 (opposite/adjacent)
x= 49.78 degrees FROM DUE WEST 180 - 49.78 = 130 .22 degrees is the COMPASS BEARING from the plane
Two ways to find the DISTANCE : 1: Pythagorean Theorem
or Sin 49.78 = opposite/hypotenuse = 136/hypotenuse
136/ (sin 49.78) = hypotenuse (the DISTANCE) = 178.11 miles
+36919 To find the ANGLE from the airplane to the second radio station:
tan x = 136/115 (opposite/adjacent)
x= 49.78 degrees FROM DUE WEST 180 - 49.78 = 130 .22 degrees is the COMPASS BEARING from the plane
Two ways to find the DISTANCE : 1: Pythagorean Theorem
or Sin 49.78 = opposite/hypotenuse = 136/hypotenuse
136/ (sin 49.78) = hypotenuse (the DISTANCE) = 178.11 miles
+128731 The two given distances are legs of a right triangle.....the distance that the plane is from the second station is just the hypotenuse of a right triangle......and this distance =
sqrt ( 115^2 + 136^2 ) = about 178.1 miles
The angle we are interesed in is the one with the plane at its vertex.......this is given by
arctan (136/115) = about 49.78°
Since bearing is measured clockwise from a north-south line.......the bearing of the second station from the airplane =
[270 + 49.78]° = 319.78°
