F.3 Trigonometry Problem

a)
∠XBY=52°+38°=90°
∴XB⊥BY (converse of Pyth theorem)

XB^2 + BY^2 = XY^2 (Pyth theorem)
(AB / tan 11°)^2 + (AB / tan 25°)^2 = 4.5^2
AB^2 [ 1/tan^2 (11°) + 1/tan^2 (25°) ] = 20.25
AB^2 = 20.25 / [ 1/tan^2 (11°) + 1/tan^2 (25°) ]
AB^2 ≈ 0.651851746
AB ≈ 0.807373362 = 0.807 km (cor to 3 sig fig)

b)
tan ∠XYB = XB / YB
tan ∠XYB = (AB/tan 11°) / (AB/tan 25°)
tan ∠XYB = tan 25° / tan 11°
∠XYB = 67.3712°

∴The whole circle bearing of ship X from ship Y
=360°-67.3712°-38°
=255 (cor to 3 sig fig)

2014-06-06 23:56:35 補充：
=255° (cor to 3 sig fig)