F.3 maths--compass bearing

Carrot

2011-06-16 6:13 pm

A and B are two cities 100km apart. The compass bearing of B from A is S30E. At noon Andrew and Billy ride bicycles and leave cities A and B respectively.
Andrew rides due south at a speed of 15km/h. while Billyrides due north at a speed of 18km/h. Find the compass bearing of Billy from Andrew at 2:00p.m. Ccorrect nearest 0.1degree)

回答 (1)

Godfrey

2011-06-16 8:26 pm

✔ 最佳答案

A
|
A2

C B2
|
D B

Andrew moves from A to A2 (30 km) and Billy moves from B to B2 (36 km) in 2 hours.
AA2 = 15 km/h x (2h) = 30 km
BB2 = 18 km/h x (2h) = 36 km
CD = BB2 = 36 km
AB = 100 km
Angle DAB = 30°.
DB = 100 km x sin 30° = 100 km x 0.5 = 50 km
CB2 = DB = 50 km
AD =100 km x cos 30° = 100 km x 0.866 = 86.6 km
A2C = AD – AA2 – CD = 86.6 km – 30 km – 36 km = 20.6 km
Tan angle CA2B2 = CB2/A2C
Tan angle CA2B2 = 50 km/20.6 km = 2.42718
Angle CA2B2 = tan^-1(2.42718) = 67.6°

Compass bearing of Billy from Andrew at 2:00 p.m. is S 67.6° E

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