Question

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

Sonny is 153ft, the distance Sam and Sal is 201ft, and the distance between Sonny
and Sal is 175ft, what is the angle of Sonny's line of sight to both Sam and Sal to the
nearest whole degree?
a. 25°
b. 75°
c. 57°
d. 123°

Answer 1

Explanation:

Answer 2

b. 75°

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 = (-13643)/(-53550)`

`\cos B = 0.254771242`

`B = \cos^(-1) 0.254771242`

`B = 75^\circ`

Answer: b. 75°