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:
[tex]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[/tex]
Degree to adjust its route at point Y = 180° - 112.12° = 67.88°
It needs to adjust by 67.88° at point Y
