Question

24. Sam, Sonny and Sal are camping in their tents. If the distance between Sam and

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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.

$b^2 = a^2 + c^2 - 2ac \cos B$

$201^2 = 175^2 + 153^2 - 2(175)(153) \cos B$

$40401 = 30635 + 23409 - 53550 \cos B$

$-53550 \cos B = -13643$

$\cos B = \dfrac{-13643}{-53550}$

$\cos B = 0.254771242$

$B = \cos^{-1} 0.254771242$

$B = 75^\circ$

Answer: b. 75°