Question 390210: this problem is APPLICATION OF OBLIQUES TRIANGLES: trigonometry
two ships leave the pier and the angle between their sail paths is 50 degree. an hour later , one ship travelled 300 mi. while the other has travelled 200 mi how far aprat are the ships at this time
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! this problem is APPLICATION OF OBLIQUES TRIANGLES: trigonometry
two ships leave the pier and the angle between their sail paths is 50 degree. an hour later , one ship travelled 300 mi. while the other has travelled 200 mi how far aprat are the ships at this time.
When given two sides and the included angle in a triangle, use the Law of Cosine to find the third side.
In this problem the two sides are 200 miles and 300 miles and the included angle is 50 deg.
label the two sides a & b and the third side,c.
c^2=a^2+b^2-2ab Cos 50 deg.
c^2=200^2+300^2-2*200*300 cos50 deg
=40000+90000-120000*cos 50
=130000-77135=52865
c=sqrt(52685)=230 miles
ans: After one hour, the ships are 230 miles apart
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