Question

A man starts at p and travels 5km on a bearing 040 degree to point q he then travels 5km on a bearing 210 degree to r find the bearing and distance of r from p

Answer 1

Following your description you should get a triangle with sides 5 and 5 and an angle of 20° between them, so use the cosine law:
r^2 = 5^2 + 5^2 - 2(5)(5)cos20
= 3.01536...
r = 1.7364..

could have dropped a perpendicular and then
sin10 = (r/2) / 5
r = 1.7364... (notice the same answer, that's encouraging)

you now have enough data to find the missing angles

Answer 2

Hard question ❓