數學三角學的應用問題

11.
ΔTYZ中：
tan∠TZY = TY/YZ
tan27° = (3 m)/YZ
YZ = 3/tan27° m

ΔXYZ中，根據正弦定律：
sin∠YXZ/YZ = sin∠YZX/XY
sin12°/(3/tan27°) = sin∠YZX/24
sin∠YZX = 8sin12°tan27°
∠YZX = 57.9°

57.9° + 12° = 69.9°
由Z測得T的方位 = S69.9°W


= = = = =
14.
(a)
ΔXBY中：
∠BXY = 90° - 60° = 30°
∠BYX = 90° - 30° = 60°

三角形內角和：
∠XBY + ∠BXY + ∠BYX = 180°
∠XBY + 30° + 60° = 180°
∠XBY = 90°

(b)
ΔXBY中：
sin∠BXY = BY/XY
sin30° = BY/(24 km)
BY = 24 sin30° km
BY = 12 km

ΔABY中：
tan∠AYB = AB/BY
tan10° = AB/(12 km)
AB = 12tan10° km
AB = 2.1 km

(c)
ΔXBY中：
cos∠BXY = BX/XY
cos30° = BX/(24 km)
BX = 24cos30° km

ΔABX中：
tan∠AXB = AB/BX
tan∠AXB = (12tan10°)/(24cos30°)
∠AXB = 5.8°
由X測得飛機A之仰角 = 5.8°