SOLUTION: A ship traveling a straight course sights a lighthouse at an angle of A=56.0 deg as shown in figure340. after traveling another B=3.49 mi, the lighthouse is at an angle of C=58.5 d

Algebra ->  Proportions  -> Lessons -> SOLUTION: A ship traveling a straight course sights a lighthouse at an angle of A=56.0 deg as shown in figure340. after traveling another B=3.49 mi, the lighthouse is at an angle of C=58.5 d      Log On


   

Question 950213: A ship traveling a straight course sights a lighthouse at an angle of A=56.0 deg as shown in figure340. after traveling another B=3.49 mi, the lighthouse is at an angle of C=58.5 deg. Determine x and y.
Figure 340 address
http://tech2.buffalostate.edu/classes/300/figs/fig340.jpg
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28A%29=y%2F%28x%2BB%29 the two unknowns are used.
sin%28C%29=y%2Fx the two unknowns are used.
The only needed unknown variables are x and y.

Two ways to continue.

y=%28x%2BB%29tan%28A%29
-
Substitute into the C equation.
sin%28C%29=%28x%2BB%29tan%28A%29%2Fx
x%2Asin%28C%29=%28x%2BB%29tan%28A%29
x%2Asin%28C%29=x%2Atan%28A%29%2BB%2Atan%28A%29
x%2Asin%28C%29-x%2Atan%28A%29=B%2Atan%28A%29
%28sin%28C%29-tan%28A%29%29%2Ax=B%2Atan%28A%29
highlight_green%28x=%28B%2Atan%28A%29%29%2F%28sin%28C%29-tan%28A%29%29%29


You can also now use the symbolic solution for x to obtain the symbolic solution for y using y=%28x%2BB%29tan%28A%29;
y=%28%28B%2Atan%28A%29%29%2F%28sin%28C%29-tan%28A%29%29%2BB%29tan%28A%29


Plug in all the values A, B, C, and evaluate x and y.