Answer:
Angle between main street and birch avenue is approximately equal to 41°.
Step-by-step explanation:
Given: Length of Birch Avenue, a = 115 m
Length of State Street , b = 75 m
To find: Angle between Main Street and Birch Avenue.
By using Pythagoras theorem, we find value of c.
a² = b² + c²
115² = 75² + c²
c² = 13225 - 5625
c² = 7600
c = √7600
c = 87.18 (approx.)
Now using Law of Cosines,
b² = a² + c² - 2ac × cos C
75² = 115² + 87.18² - 2 × 115 × 87.18 × cos C
-15200 = - 20050.94 × cos C
cos C = 0.76
cos C = cos 40.54
C = 40.54 ≈ 41 (approx.)
Therefore, Angle between main street and birch avenue is approximately equal to 41°.
