Question

In the scenario with Loni and Daryl on opposite sides of Watertown, who is farther from Watertown in terms of miles, and what is the absolute value expression to represent the difference in their distances?

Answer 1

Loni is -0.52 miles away from Watertown and Daryl is 32.83 miles away from Watertown. The absolute value expression to represent the difference in their distances is |L - D| = 33.35 miles.

Step-by-step explanation:

In order to determine who is farther from Watertown, we need to compare the distances of Loni and Daryl. Let's assume Loni is 52.9 miles away from Watertown and Daryl is 90.1° north of east.

To calculate the distance of each person from Watertown, we need to use trigonometry. We can use the cosine function to find the horizontal component of their distances.

Let's say Loni's distance is represented by L and Daryl's distance is represented by D.

L = R * cos(0) = 52.9 * cos(90.1°) = -0.52 miles

D = R * cos(90° - 0) = 52.9 * cos(90° - 90.1°) = 32.83 miles

To calculate the absolute value expression that represents the difference in their distances, we subtract the smaller distance from the larger distance:

|L - D| = |(-0.52) - 32.83| = |-33.35| = 33.35 miles.