1. ## bearing

kindly answer the bearing... i got the angle at forest island but i dont know how to get the bearing in from forst island to home port..

the bearing should be South East, but what degrees

2. Hello, aeroflix!

A fisherman leaves his homeport and heads in the direction $\displaystyle N\,70^o\,W$.
He sails 30 miles and reaches Egg Island.

The next day he sails $\displaystyle N\,10^o\,E$ for 50 miles to Forest Island.

(b) Find the bearing from Forest Island back to his homeport.

In my diagram, I omitted the distances (they wouldn't fit).

Code:
            F
♥
Q    *:
:   * :*
:10*  :
: *   : *   P
:*    S     :
E ♥100     *  :
: *         :
:70 *     * :
:     *   70:
R       *  *:
* :
♥ H

The homeport is $\displaystyle H.$

He sails 30 miles to $\displaystyle E.$
. . $\displaystyle \angle PHE = \angle HER = 70^o,\;HE = 30$

Then he sails 50 miles to $\displaystyle F.$
. . $\displaystyle \angle QEF = 10^o \quad\Rightarrow\quad \angle FEH = 100^o,\;\; EF = 50$

I assume that part (a) asked for the distance from $\displaystyle F$ to $\displaystyle H.$

. . $\displaystyle FH^2 \;=\;30^2 + 50^2 - 2(30)(50)\cos100^o \;=\;3920.944533$

Hence: .$\displaystyle FH \;=\;62.61744592 \;\approx\;62.62$

Now we determine $\displaystyle \angle FHE.$

. . $\displaystyle \cos(\angle FHE) \;=\;\dfrac{30^2 + 62.62^2 - 50^2}{2(30)(62.62)} \;=\; 0.61781763$

Hence: .$\displaystyle \angle FHE \;=\;52.84305918^o \;\approx\;51.8^o$

Then:. . $\displaystyle \angle PHF \;=\;70^o - 51.8^o \;=\;18.2^o$

Note that: .$\displaystyle \angle SFH = \angle PHF$

Therefore, the bearing is: .$\displaystyle S\,18.2^o\,E$

3. thanks soroban.. now i realize that there are some same angles