Maths Question- PLEASE HELP

[hellymyname]

1- A boat crosses the start line of a race on a bearing of 340 degrees. After 700m, it rounds a buoy and sails on a bearing of 038 degrees. When it is due North of its start, how far has it sailed altogether?

2- The bearing of Y from X is 205 degrees. The bearing of Z from Y is 315 degrees, and the bearing of X from Z is 085 degrees. If XZ = 4km, find the distance of XY.

Please show working as well, thanks!

[Jumbuck]

How about

1) 700 x (cos20 + (sin20 x tan52))
2) 4 x tan50 / (cos60 x (tan50 + tan60))

Either extremely brilliant or complete bs - you decide...

[Etch]

Use the Sine Rule in both cases:

1)
Let x be the distance sailed from the buoy to the position due North of the start. Then
x/sin(20) = 700/sin(38)
So total distance sailed = 700 + x = 700*(1 + sin(20)/sin(38)) = 1089 m (to the nearest metre)

2)
Angle XYZ = 70 degrees, angle XZY = 50 degrees so
XY/sin(50) = 4/sin(70)
Thus XY = 4*sin(50)/sin(70) = 3.26 km