Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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°

Sagot :

Answer:

Step-by-step explanation:

mathstudent55

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°

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.