An aircraft flies 50 km on a bearing of 065 degrees, then 80 km on a bearing of 040 degrees. Calculate the total distance of the aircraft from its starting point.

Step 1: Calculate the North and East components for the first leg. The aircraft flies 50 km on a bearing of 065^. Let N_1 be the North component and E_1 be the East component. N_1 = 50 (65^) E_1 = 50 (65^) Using a calculator: N_1 ≈ 50 × 0.4226 = 21.13 km E_1 ≈ 50 × 0.9063 = 45.32 km Step 2: Calculate the North and East components for the second leg. From the end of the first leg, the aircraft flies 80 km on a bearing of 040^. Let N_2 be the North component and E_2 be the East component. N_2 = 80 (40^) E_2 = 80 (40^) Using a calculator: N_2 ≈ 80 × 0.7660 = 61.28 km E_2 ≈ 80 × 0.6428 = 51.42 km Step 3: Calculate the total North and East displacement from the aerodrome A. Let N_total be the total North displacement and E_total be the total East displacement. N_total = N_1 + N_2 = 21.13 km + 61.28 km = 82.41 km E_total = E_1 + E_2 = 45.32 km + 51.42 km = 96.74 km Step 4: Calculate the distance of the aircraft from A. The distance from A is the hypotenuse of the right-angled triangle formed by N_total and E_total. Distance = sqrt(N_total)^2 + E_total^2 Distance = sqrt((82.41)^2 + (96.74)^2) Distance = sqrt(6791.4081 + 9358.6276) Distance = sqrt(16150.0357) Distance ≈ 127.08 km Rounding to one decimal place: Distance ≈ 127.1 km Step 5: Calculate the bearing of the aircraft from A. Let be the angle measured clockwise from the North line. () = E_totalN_total () = (96.74)/(82.41) () ≈ 1.1739 = (1.1739) ≈ 49.57^ Since both N_total and E_total are positive, the aircraft is in the North-East quadrant, so the bearing is simply this angle. Rounding to one decimal place and expressing as a 3-digit bearing: Bearing ≈ 049.6^ The distance of the aircraft from A is 127.1 km and its bearing from A is 049.6^. Last free one today — make it count tomorrow, or type /upgrade for unlimited.