50 points! main street, and birch avenue (115m) intersect to form a right triangle. what angle does main street make with birch avenue? enter your answer in the box. round only your final answer to the nearest degree. (state street is 75m)

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°.

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