17.5 CHAPTER 17. TRIGONOMETRY
A� �B
�
C127 ◦ 255 ◦
SOLUTION
We can see that the two lighthouses and the boat form a triangle. Since we know the dis-
tance between the lighthouses and we have two angles we can use trigonometry to find the
remaining two sides of the triangle, the distanceof the boat from the twolighthouses.
A� �B
�
C37 ◦^15 ◦
128 ◦
0 , 67 kmWe need to know the lengths of the two sides AC and BC. We can use the sine rule to
find our missing lengths.
BC
sinAˆ=
AB
sinCˆBC =
AB. sinAˆ
sinCˆ
=
(0,67)sin(37◦)
sin(128◦)
= 0,51 kmAC
sinBˆ=
AB
sinCˆAC =
AB. sinBˆ
sinCˆ
=
(0,67)sin(15◦)
sin(128◦)
= 0,22 km