Posted by **helpisneeded** on Thursday, January 27, 2011 at 2:47pm.

Two Boats left the harbour at the same time. One travelled at 10km/h on a bearing of N47°E. The other travelled at 8km/h on a bearing of N79°E. How far apart were the boats after 78 mins? Round the distance to the nearest tenth of a kilometer. Use trigonometry.

- Math -
**helper**, Thursday, January 27, 2011 at 5:05pm
To understand this you really need to sketch this out.

Think of the x/y axis on a graph, with the y-axis as North and the x-axis as East. Both boats are traveling from the North (top of the y-axis), toward East (down toward the x-axis).

The first bearing, forms a 47 deg. angle with the y-axis and the second bearing, goes a little further forming a 79 deg. angle with the y-axis.

The triangle formed, (I labeled ABC), with A at the origin, side c (between angle A and angle B), side b (between angle A and angle C) and side a (between angle B and angle C).

You need to find side a, the distance between the boats.

1 km/h / 60 min = 0.01667 km/min

First boat 10 km/h * 0.01667 = 0.1667 km/min * 78 min = 13 km

Second boat 8 km/h * 0.01667 = 0.1333 km/min * 78 min = 10.4 km

Angle A = 79 deg - 47 deg = 32 deg.

side c = 13 km (first boat's bearing)

side b = 10.4 km (second boat's bearing)

To find side a,

a^2 = b^2 + c^2 - 2bc cos A

a^2 = 10.4^2 + 13^2 - 2(10.4)(13)cos 32d

a^2 = 108.16 + 169 - 270.4 (.8)

a^2 = 277.16 - 216.32

a^2 = 60.8 km

## Answer this Question

## Related Questions

- math - 2 boats left the harbour at the same time. One travelled at 10km/h on a ...
- maths - Two patrol boats M3 and M7 leave port at the same time.M3 heads due west...
- Math - Two boats leave whitby harbour at the same time one boat heads 18 km to ...
- trig - two ships p and q left a port at the same time. q sailed on a bearing of...
- bearing and distance - Two vehicles p and q leave a station at the same time.p ...
- math - Two ship P and Q left a port R at the same time.Q sailed on a bearing of ...
- PRE-CALC HELP - Two boats leave the same port at the same time. One travels at ...
- Math - Two boats leave a dock at the same time. One heads due east at 20 mph, ...
- Math - Two boats start out from the same dock traveling at 9 mph and 12 mph ...
- math - Two fishing boats depart a harbor at the same time, one traveling east, ...

More Related Questions