The Law of Sines

Question

Paul's dog ran out of the house. It ran 19 meters, turned and ran 12 meters, and then turned 155°to face the house. How far away from the house is Paul's dog? Round to the nearest hundredth.

___ meters

Answer 1

19 then turn and go 12, then turn 155 degrees to face the house

how far is the dog from the house?? question is a little ambiguous, but here goes a stab in the dark

19/sin155 = 12/sinD

sinD = 12sin155/19 where D=angle opposite 12

D = about 15.48 degrees

a/sin9.5 = 19/sin155

a = 19sin9.5/sin155 = about .13 meters = distance dog is from house

Law of Signs is obey all traffic signs or risk getting pulled over, maybe arrested too, headed for the county jail, and your car towed

Answer 2

the angle facing line of 19m. is 25 degrees,,,, this angle is at dog,,,25=180-155

call angle facing 12m. angle B ,,B is at house

call angle facing distance (d) angle C,,,,,angle C is juncture of 19m. and 12m. lines

sin(B)=19*sin(25)/12

C=180-25-B

d=19*sin(C)/sin(25)