SOLUTION: Two points A and B lie on opposite sides of a river. Another point C is located on the same side of the river as B at a distance of 250 ft from B. If angle ABC is 100° and angle AC

Algebra ->  Trigonometry-basics -> SOLUTION: Two points A and B lie on opposite sides of a river. Another point C is located on the same side of the river as B at a distance of 250 ft from B. If angle ABC is 100° and angle AC      Log On


   



Question 964721: Two points A and B lie on opposite sides of a river. Another point C is located on the same side of the river as B at a distance of 250 ft from B. If angle ABC is 100° and angle ACB is 20°, find the distance across the river from A to B.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Find angle BAC since the angles sum to 180.
BAC%2B20%2B100=180
BAC=60
Use the law of sines,
250%2Fsin%2860%29=X%2Fsin%2820%29
X=250%28sin%2820%29%2Fsin%2860%29%29
X=250%280.3949%29
X=98.7 ft