sine and cosine

[lovely_nancy]

could I get help with the diagram of the following two questions should be fine with the rest... Thanks

A yacht sets off from A and sails 3km on a bearing of 045degrees to a point B.
It then sails 1km on a bearing of 322degrees to a point C.


A helicopter leaves a point P and flies on a bearing of 162degrees for 3km to a point Q,
and then due west to a point R which is on a bearing of 220degrees from P

 

[mmm4444bot]

If my scribbles are correct, points A, B, and C form a triangle with the following.

Angle ABC is 97 degrees

Side AB is 3

Side BC is 1

(I hear The Law of Cosines coming.)

I'm having trouble drawing a triangle with points P, Q, and R.

Please check the information that you posted for that exercise.

 

[soroban]

Hello, lovely_nancy!

A yacht sets off from A and sails 3 km on a bearing of 045 degrees to a point B.
It then sails 1km on a bearing of 322 degrees to a point C.

I agree with mmm444bot . . .

\(\displaystyle \text{A bearing of }332^o\text{ is equivalent to a heading of }N38^oW.\)
. . \(\displaystyle \text{And hence: }\:\angle B = 97^o.\)

            C     :
            o     :
              *38d:
             1  * :
      :           o B
      :         * :
      :       *45d:
      :     * 3   :
      :45d*       :
      : *
      o
      A

A helicopter leaves a point P and flies on a bearing of 162 degrees for 3 km to a point Q,
and then due west to a point R which is on a bearing of 220 degrees from P.

\(\displaystyle \text{A bearing of }162^o\text{ is equivalent to a heading of }S18^oE\)

                :
                :
                :
              P o 162d
                :*
                : *
                :  * 3
                :18d*
                :    *
                :     o Q
                :

\(\displaystyle \text{A bearing of }220^o\text{ from }P\text{ is equivalent to a heading of }S40^oW.\)

                :
                :
               P:
                o 180d
              * : 
            *40d:
          *     : 
        *       :
      *
  R o

The diagram looks like this:

                :
                :
              P :
                o
              * :*
    :       *40d: *
    :     *     :  * 3
    :40d*       :18d*
    : * 30d     :    *
  R o - - - - - - - - o Q