Problema Solution
A hike parks his car and then hikes in the woods for 3 miles. he then turns, thinking that he is walking back to his car and walks for 4 miles. When he stops, he finds that he is 2 miles from his car. Draw the triangle and then find the angle between the hikers 2 paths.
Answer provided by our tutors
At the moment we don't have the option the solve problems by drawing.
let a = 3 mi, b = 4 mi and c = 2 mi are sides and B = the angle opposite side b
we will use the Law of Cosines to find the angle B:
b^2 = a^2 + c^2 - 2ac*cos(B)
cos(B) = (a^2 + c^2 - b^2)/(2ac)
cos(B) = (3^2 + 2^2 - 4^2)/(2*3*2)
cos(B) = - 1/4
B = arccos(-1/4)
B = 104.4 degrees