Answer:
b. 75°
Step-by-step explanation:
Draw a triangle. Write a person name and a point name (a letter) at each vertex: Sam A, Sonny B, and Sal C at the vertices.
Write the distances as AB = c = 153 ft; AC = b = 201 ft; BC = a = 175 ft.
We are looking for angle B.
Since we have a triangle with three side lengths and no angle measures, we use the Law of Cosines.
[tex] b^2 = a^2 + c^2 - 2ac \cos B [/tex]
[tex] 201^2 = 175^2 + 153^2 - 2(175)(153) \cos B [/tex]
[tex] 40401 = 30635 + 23409 - 53550 \cos B [/tex]
[tex] -53550 \cos B = -13643 [/tex]
[tex] \cos B = \dfrac{-13643}{-53550} [/tex]
[tex] \cos B = 0.254771242 [/tex]
[tex] B = \cos^{-1} 0.254771242 [/tex]
[tex] B = 75^\circ [/tex]
Answer: b. 75°
