Question

A man walks 3 km due east and then 5 km northeast, how do you find his distance and bearing from his original position?

Answer 1

`7.43` km `28.4^@` North of East (approx.)

Explanation:

Using the Law of Cosines
`color(white)("XXX")c=sqrt(a^2+b^2-2cos(/_C))`
evaluated using a calculator
`color(white)("XXX")c~~7.4305...`

Using the Law of Sines
`color(white)("XXX")sin(/_B)=5/cxxsin(135^@)`
evaluated using a calculator
`color(white)("XXX")sin(/_B)~~0.4758...`
and
`color(white)("XXX")/_B=arcsin(0.4758...)~~28.412^@`