Since I have no diagram, I make the following assumptions.
We can view the scene from high above, so the elevations of A and B make no difference.
C is between A and B, but not on the line AB.
The fire at F is on the opposite side of AB from C.
So, we can use the law of cosines to find that in triangle ABC,
∠B = 46.56°
In triangle ABF,
∠F = 56°
so BF can be found using the law of sines, to be
BF = 2.97 (call it 3)
So, the displacement of F from C is
(2cos46.56°-3cos86°,2sin46.56°+3sin86°) = (1.17,4.45)
So, the angle θ of F from CB is
θ = arctan(4.45/1.17)-56° = 19.27°
If my assumptions were in error, I'm sure you can fix them and redo the math,
Two lookout towers are situated on mountain tops A and B, 4 mi from each other. A helicopter firefighting team is located in a valley at point C, 3 mi from A and 2 mi from B. Using the line between A and B as a reference, a lookout spots a fire at an angle of α = 38° from tower A and β = 86° from tower B. See the figure. At what angle, measured from CB, should the helicopter fly in order to head directly for the fire? (Round your answer to two decimal places.)
1 answer