Answer: Approximately 20.49
Explanation:
Jim’s dog is approximately 20.49 yards away from the house. To find the distance of Jim’s dog from the house after its movements, we can use the concept of vectors and apply the Pythagorean theorem. The dog initially ran 19 yards and then turned 7 yards, forming a right triangle. The angle between the two sides is 75°. Using trigonometry, we can find the length of the hypotenuse which is the distance between Jim’s dog and the house.
The formula for finding the hypotenuse is:
h = sqrt(a^2 + b^2)
where h is the hypotenuse, a is one side of the triangle, and b is the other side.
We can use this formula to find the distance between Jim’s dog and the house:
h = sqrt(19^2 + 7^2 - 2197*cos(75°)) = 20.49 yards (rounded to two decimal places)12.
I hope that helps!