Question

Boat A is 20 km from port on a true bearing of

025° and boat B is 25 km from port on a true
bearing of 070°. Boat B is in distress. What
bearing (to the nearest degree) should boat A
travel on to reach boat B?

Answer 1

Hi,

Explanation:

We are going to use in the triangle PAB:

1) Al Kashi theorem:

`AB^2=PA^2+PB^2-2*PA*PB*cos(\widehat{BPA})\\=20^2+25^2-2*20^*25*cos(45^o)\\=317,8932...\\AB=17.8296\ km`

2) law of sinus:

`(sin(45^o))/(AB) =\frac{sin(\widehat{PAB})}{PB}\\\\sin(\widehat{PAB})=(sin(45^o)*25)/(17.8296)}=82.5159^o\\ \\bearing= 25^o +25^o - 82.5159=122.48137^o\\`

answer 122°