Based on the given data, we know that Janice is 63 inches tall and the angle of depression to the dog is 65º.
To find the distance between Janice and the dog, we'll use the properties of tangent. Tangent of an angle in a right triangle is the ratio of the side opposite to the angle to the side adjacent to the angle. In this scenario, the angle of depression is 65º, Janice's height is the side opposite to the angle and the distance to the dog is the side adjacent to the angle. So:
tan(65º) = Janice's height / Distance to the dog
Rearranging the equation to solve for the distance:
Distance to the dog = Janice's height / tan(65º)
We plug in the given values:
Distance to the dog = 63 inches / tan(65º)
Solving the equation, we find that the distance to the dog is approximately 29.38 inches.
Now, we know that the dog will be startled if Janice is within 48 inches of it. Comparing the distance from Janice to the dog with the startle distance, we see that 29.38 inches is indeed less than 48 inches, meaning that the dog will indeed be startled.
So, the answers to the questions are: Janice is roughly 29.38 inches away from the dog, and yes, the dog will be startled.