Two boats leave the same port at the same time One travels a

Two boats leave the same port at the same time. One travels at a speed of 31 mi/h in the direction N 50° E, and the other travels at a speed of 26 mi/h in a direction S 70° E (see the figure). How far apart are the two boats after 1 h? (Round your answer to the nearest mile.) N 50 E 50* 70 S70 E tS Need Help? 10. Airport B is 300 mi from airport A at a bearing N 50° E (see the figure). A pilot wishing to fly from A to 8 mistakenly flies due east at 250 mi/th for 40 min, when he notices his Airport B 300 mi

Solution

angle between the two boats are 180 - (50 + 70) = 60 degrees

distance travelled by 1st boat in 1 hr = 31 miles

distance travelled by boat 2 in 1 hour = 26 miles

applying law of cosines to find the distance between two boats after 1 hour

d^2 = 31^2 + 26^2 - 2 (31)(26) cos 60

d = 28.8271   

hence , the boats are 29 miles apart