Your diagram should show that the angle between their paths is 72°
In 2 hours, one will have gone 30 km and the other 40 km.
by the cosine law:
x^2 = 30^2 + 40^2 - 2(30)(40)cos72°
= 1758.3592...
x = √.... = 41.93...
or
you should have 2 right-angled triangles, since you said one ship was north of the other after 2 hours.
distance between them = 40sin27° + 30sin45° = 39.37... NOT the same as above
Notice the difference! explained by the fact that if each goes along their stated
paths for 2 hours, the first ship will NOT be directly north of the 2nd.
This would invalidate my second method, where it was assumed we had a vertical line
The stated fact of one ship being north of the other is not needed in my cosine law
method, so that answer is correct. The second method is actually incorrect.
If you use the sine law, it will show that the angle opposite the 40 side is 42.88° not 63°
Two boat leave a port at the sametime.The first travel at 15km/hr on a bearing of 135° while the second travel at 20km/hr on a bearing 063°.If after 2hours,the second boat is directly north of the first boat calculate their distance apart.(Answer 41.9). Showing the diagram and working showing diagram and answer
1 answer
1 answer