SOLUTION: Please help with this math word problem!! A pet's collar contains a transmitter that is helping its owners find the lost animal. From positions 250 m apart, the searchers can dete

Click here to see ALL problems on Triangles

Question 1129902: Please help with this math word problem!!
A pet's collar contains a transmitter that is helping its owners find the lost animal. From positions 250 m apart, the searchers can detect the transmitter at angles 87 and 53 from the straight line between the searchers. How far is each searcher from the lost pet?
I drew out the triangle but I can't seem to find out if it's correct.
Thanks for any help!

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
you would use the law of sines to find the answer to this question.
first draw a straight line between the searchers.
that line is 250 meters long.
let one end of this straight line be point A.
let the other end of this straight line be point C.
draw an angle of 87 degrees from point A.
draw an angle of 53 degrees from point B.
the lines will intersect at point C.
that point is where the cat is.
your triangle is ACB, where point A is the location of one of the searchers and point C is the location of the cat and point B is the location of the other searcher.
angle A is 87 degrees, angle C is 40 degrees, angle B is 53 degrees.
the sum of the angles is 180 degrees, as it should be.
the length of side AB is 250 meters.
from there, you can use the law of sines to find the length of the other sides of the triangle.
the side that is 250 meters long (AB) is called side c because it is opposite angle C.
the side opposite angle A is called side a.
the side opposite angle B is called side b.

my diagram is shown below:

once you've drawn your diagram, then use the law of sines to find the length of the other two sides of the triangle.

law of sines says a / sin(A) = b / sin(B) = c / sin(C).

i truncated the answers to 5 decimal places in the diagram.
this allows you to round to 2 or 4 decimal places if required.
the answered displayed in the calculator are.
a = 388.3979404
b = 310.614073