SOLUTION: Q.3 Alexa and Luke left the dock from the same point in two separate boats to place markers for a boat race. Alexa rowed 85 m and Luke rowed 102 m to place their markers. Find the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Q.3 Alexa and Luke left the dock from the same point in two separate boats to place markers for a boat race. Alexa rowed 85 m and Luke rowed 102 m to place their markers. Find the      Log On


   

Question 1173416: Q.3 Alexa and Luke left the dock from the same point in two separate boats to place markers for a boat
race. Alexa rowed 85 m and Luke rowed 102 m to place their markers. Find the angle in between their
two paths, given that the distance between the two markers is 127 m
Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.

You are given two sides of the triangle a= 85 m  and  b= 102 m,

and the third side  c= 127 m opposite to the angle under consideration.


You need to find the angle gamma  between the sides  "a"  and  "b".


Use the Cosine law 


    c^2 = a%5E2+%2B+b%5E2+-+2bc%2Acos%28gamma%29.


From this formula,  find  


    cos%28gamma%29 = %28c%5E2+-+a%5E2+-+b%5E2%29%2F%282bc%29 = %28127%5E2+-+85%5E2+-+102%5E2%29%2F%282%2A85%2A102%29 = -0.08651.


Then  cos%28gamma%29 = arccos(-0.08651) = 1.6574 radians = 95 degrees (approximately).


ANSWER.  The angle is about 95 degrees.

Solved.