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?

Answer 1

Answer:

67.88°

Step-by-step explanation:

If three sides of a triangle are known and you want to determine one angle, this can be done using cosine rule.

Given sides x, y, and z and the angle Y is opposite to side y, the cosine formula is given as:

y² = x² + z² - 2xzcosY

For this problem, x = 400 miles, y = 599 miles, z = 320 miles.

Using the cosine formula:

$y^2=x^2+z^2-2xzcos(Y)\\Substituting:\\599^2=400^2+320^2-2(400)(320)cos(Y)\\2(400)(320)cos(Y)=400^2+320^2-599^2\\256000cos(Y)=-96401\\cos(Y)=-0.3766\\Y=cos^{-1}(-0.3766)\\Y=112.12^0$

Degree to adjust its route at point Y = 180° - 112.12° = 67.88°

It needs to adjust by 67.88° at point Y