Find the surface area pls
2 answers:
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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°
