Question

An airplane started at point X, traveled 320 miles to point Y, adjusted its route and traveled another 400 miles to point Z. If the airplane is currently 599 miles from its starting position at point X, by how many degrees did it adjust its route at point Y? (Round your answer to the nearest degree if necessary. Do not enter the degree symbol.)

Answer 1

Given:

To find the angle Y, Use the cosine rule,

`\begin{gathered} (^{}ZX)^2=(ZY)^2+(YX)^2-2(ZY)(YX)\cos Y \\ 599^2=400^2+320^2-2(400)(320)\cos Y \\ 358801-262400=-256000\cos Y \\ -(96401)/(256000)=\cos Y \\ Y=\cos ^(-1)(-(96401)/(256000)) \\ Y=112.1212^(\circ) \end{gathered}`

To find the angle where the airplane adjust its route to point Y,

It form the supplementary angle.

Answer: The angle where the airplane adjust its route to point Y is 67.88 degree (68).