# Thread: Urgent Trigonometry help needed

1. ## Urgent Trigonometry help needed

Radar stations A and B are on an east-west line, 3.7km apart. Station A detects a plane at C with a bearing of 61 degrees. Station B also detects the plan with a bearing of 331 degrees. Find the distance from A to C.

I have drawn many different diagrams but none seem to be the right one. Could someone please help me?

2. Hello. lax600!

Are you sure you understand bearings?
They are measured clockwise from due North.

Radar stations $A$ and $B$ are on an east-west line, 3.7 km apart.
Station $A$ detects a plane at $C$ with a bearing of 61°.
Station $B$ also detects the plane with a bearing of 331°.
Find the distance from $A$ to $C$.
Try it with this diagram . . .
Code:
                    C
*
P             *  *      Q
:           *     *     :
:         *        *    :
:       *           *29°:
:     *              *  :
:61°*                 * :
: * 29°            61° *:
A * - - - - - - - - - - - * B
3.7

We are given: . $\angle PAC = 61^o$
. . Hence: . $\angle CAB = 29^o$

We see that: . $\angle QBC = 29^o$
. . Hence: . $\angle CBA = 61^o$

Then: . $\angle C \:=\:180^o - 29^o - 61^o \:=\:90^o$
. . $\Delta ABC$ is a right triangle.

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

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

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# radar stations a and b are 3.7 miles apart .

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