Question

Julia is skiing along a circular ski trail that has a radius 2.5 km long. She starts at the 3-o'clock position (the easternmost point on the trail) and travels in the counterclockwise direction. Julia stops skiing when she is 1.99 km east and 1.513 km north of the ski trail's center. Imagine an angle with its vertex at the ski trail's center that subtends Julia's path. What is the measure of the angle in degrees?

Answer 1

To find the measure of the angle in degrees, we can use trigonometry. By calculating the distance from Julia's stopping point to the ski trail's center using the Pythagorean theorem and then finding the angle using the inverse tangent function, we can determine that the measure of the angle is approximately 37.21 degrees.

Step-by-step explanation:

To find the measure of the angle in degrees, we need to find the angle that Julia's path subtends at the center of the ski trail. Given that Julia stops skiing at coordinates (1.99 km east, 1.513 km north) from the ski trail's center, we can use trigonometry to find the angle.

First, let's calculate the distance of Julia's stopping point from the ski trail's center using the Pythagorean theorem. The distance is given by:

d = sqrt((1.99 km)^2 + (1.513 km)^2) = 2.541 km

Next, we can find the angle using the inverse tangent function:

angle = tan^(-1)(opposite/adjacent) = tan^(-1)(1.513 km/1.99 km) = 37.21 degrees

Therefore, the measure of the angle in degrees is approximately 37.21 degrees.