Question

Alicia, Britney, and Courtney go camping. They begin setting up their tents in the campground so that Alicia is 100 feet away from Britney and Britney is 115 feet away from Courtney. If the angle formed at Courtney's tent is 35 degrees, what is the angle formed at Alicia's tent?

Answer 1

To find the angle formed at Alicia's tent, we can use the law of cosines. By plugging in the given distances, we can find the angle to be approximately 79.573 degrees.

Step-by-step explanation:

To find the angle formed at Alicia's tent, we can use the law of cosines. Let's call the angle at Alicia's tent 'x'. According to the law of cosines,

c^2 = a^2 + b^2 - 2ab * cos(x)

Where c is the distance between Alicia and Courtney (115 feet) and a and b are the distances between Alicia and Britney (100 feet) and Britney and Courtney, respectively. Plugging in the values, we get:

115^2 = 100^2 + 115^2 - 2 * 100 * 115 * cos(x)

Simplifying the equation gives us:

13225 = 10000 + 13225 - 23000 * cos(x)

Subtracting 10000 from both sides and rearranging the equation, we have:

0 = 3225 - 23000 * cos(x)

Dividing both sides by 23000, we get:

cos(x) = 3225/23000

Using a calculator, we can find the value of cos(x) to be approximately 0.14022. To find the angle x, we can take the inverse cosine:

x = cos^(-1)(0.14022)

Calculating x gives us x ≈ 79.573 degrees.