Thread: Law of Sines....I think

Two lookout stations, which are 25 miles apart along the coast on a north-south line, spot an approaching yacht. One lookout station measures the direction to the yacht at N33* E, and the other station measures the direction of the yacht at S62* E. How far is the yacht from each lookout station? How far is the yacht from the coast?

I have no idea where to start for this one. Please help me!! Thanks!

Hello, suzdisp!

Did you make a sketch?

Two lookout stations, which are 25 miles apart along a north-south costline,
spot an approaching yacht.
One lookout station finds the direction to the yacht at N33°E,
and the other station finds the direction of the yacht at S62°E.

(1) How far is the yacht from each lookout station?

(2) How far is the yacht from the coast?

Code:

  -  B*
  :   |  *
  :   | 62° *   a
  :   |        *
  :   |           *
  :   |              *
  :  D* - - - - - - 85° *C
  :   |               *
 25   |             *
  :   |           *
  :   |         *
  :   |       * b
  :   |     *
  :   |33°*
  :   | *
  -  A*

Since , then: .


Law of Sines: .

. . (1)


Law of Sines: .

. . (1)


In right triangle

Therefore: . (2)