The cast of Sesame Street decided to take a camping trip. being the rebels they are, elmo, cookie monster and oscar decided to camp alone. They each have their own tent and the tents are set up in a triangle. elmo and cookie monster are 10 meters apart. The angle formed at elmo is 105 degrees. how far apart are oscar and elmo to the nearest meter?
42m
I also forgot to add that the angle formed at oscar is 30 degrees.
To find the distance between Oscar and Elmo, we can use the Law of Cosines, which relates the sides and angles of a triangle.
In this case, Elmo and Cookie Monster form a triangle with sides of 10 meters, and the angle at Elmo is 105 degrees. Let's label the distance between Elmo and Oscar as "x".
According to the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos(C)
where c is the side opposite to angle C and a and b are the other two sides.
In this case, c represents the distance between Elmo and Oscar (x), a represents the distance between Elmo and Cookie Monster (10 meters), b represents the distance between Cookie Monster and Oscar (also 10 meters), and C is the angle at Elmo (105 degrees).
So, substituting the values into the formula:
x^2 = 10^2 + 10^2 - 2 * 10 * 10 * cos(105)
To find the value of cos(105), we need to use a calculator or a trigonometric table. The cosine of 105 degrees is approximately -0.2588.
Substituting this value:
x^2 = 100 + 100 - 2 * 10 * 10 * (-0.2588)
x^2 = 200 + 515.76
x^2 = 715.76
Now, to find x, we take the square root of both sides of the equation:
x = sqrt(715.76)
x ≈ 26.77
Therefore, Oscar and Elmo are approximately 26.77 meters apart to the nearest meter.