Answer:
Angle Rome to Paris = 44.68°
Angle Paris to Berlin = 71.26°
Angle Berlin to Rome = 64.06
Step-by-step explanation:
See attachment for diagram illustration for this.
Let represent distance from Rome to Paris as a, distance from Paris to Berlin as b, and distance from Berlin to Rome as c.
Therefore we say
a = 697miles, b = 545miles, c = 734miles
To find the respectively angle formed from, Berlin to Paris to Rome, we will apply the cosine rule, which states that:
c² = a² + b² - 2abCosC
734² = 697² + 545² - 2(697*545)cosC
2(697*545)cosC = 697² + 545² - 734²
759739 cosC = 244078
cosC = 244078/759739
cosC = 0.3212
C = cos-¹0.3212
C = 71.26°
To get angle B, we will apply the sine rule, which states that:
a/sineA = b/sineB = c/sineC
Therefore we have
545/sineB = 734/sine71.26
= 545/sineB = 734/0.947
= 545/sineB = 734/0.947
= 545/sineB = 775.08
SineB = 545/775.08
B = sine-¹0.7032
B = 44.68°
Angle A = 180 - (B+C) angle in a triangle
A = 180 - (44.68 + 71.26)
A = 180 - 115.94
A = 64.06°
A = 64.06°
B = 44.68°
C = 71.26°
Angle Rome to Paris = 44.68°
Angle Paris to Berlin = 71.26°
Angle Berlin to Rome = 64.06°
Answer:
Step-by-step explanation:
The movement of the airplane can be represented using a triangle. In Triangle PRB, we are required to find Angles P, R and B.
Using Law of Cosines
[tex]cos R=\frac{p^2+b^2-r^2}{2pb} \\cos R=\frac{734^2+697^2-545^2}{2*734*697}\\R=arcCos\left(\frac{734^2+697^2-545^2}{2*734*697}\right)\\R=44.68^0[/tex]
Using law of Sines
[tex]\frac{r}{sin R}=\frac{p}{SIn P} \\\frac{545}{sin 44.68}=\frac{734}{Sin P} \\\text{Cross Multiply}\\545 X Sin P=734 X sin 44.68\\Sin P=\frac{734 X sin 44.68}{545} \\P=arcSin\left(\frac{734 X sin 44.68}{545}\right)\\P=71.26^0[/tex]
Now,
P+R+B=180 degrees (Sum of Angles in a Triangle)
[tex]71.26^0+44.68^0+B=180^0\\B=180^0-[71.26^0+44.68^0]\\B=64.06^0[/tex]
