Hello. lax600!

Are you sure you understand bearings?

They are measured clockwise from due North.

Radar stations $\displaystyle A$ and $\displaystyle B$ are on an east-west line, 3.7 km apart.

Station $\displaystyle A$ detects a plane at $\displaystyle C$ with a bearing of 61°.

Station $\displaystyle B$ also detects the plane with a bearing of 331°.

Find the distance from $\displaystyle A$ to $\displaystyle C$. Try it with this diagram . . . Code:

C
*
P * * Q
: * * :
: * * :
: * *29°:
: * * :
:61°* * :
: * 29° 61° *:
A * - - - - - - - - - - - * B
3.7

We are given: .$\displaystyle \angle PAC = 61^o$

. . Hence: .$\displaystyle \angle CAB = 29^o$

We see that: .$\displaystyle \angle QBC = 29^o$

. . Hence: .$\displaystyle \angle CBA = 61^o$

Then: .$\displaystyle \angle C \:=\:180^o - 29^o - 61^o \:=\:90^o$

. . $\displaystyle \Delta ABC$ is a right triangle.

We have: .$\displaystyle \sin 61^o \:=\:\frac{AC}{3.7}$

Therefore: .$\displaystyle AC \:=\:3.7\sin61^o \:=\:3.236092916$ km.