Question

Vanessa is skiing along a circular ski trail that has a radius of 2.5 km. She starts at the 3-o'clock position and travels in the CCW direction. Vanessa stops skiing when she is 1.244 km to the right and 2.169 km above the center of the ski trail. Imagine an angle with its vertex at the center of the circular ski trail that subtends Vanessa's path.
How many radians has the angle swept out since Vanessa started skiing?

Answer 1

Answer:

1.05 radians

Step-by-step explanation:

Given that Vanessa is skiing along a circular ski trail that has a radius of 2.5 km. She starts at the 3-o'clock position and travels in the Counter Clockwise direction.

She stops skiing when she is 1.244 km to the right and 2.169 km above the center of the ski trail.

This can be represented as (1.244, 2.169) on a circle of radius 2.5 km.

From the coordinate point (1.244, 2.169) derived, x=1.244 and y=2.169.

By the definition of tangent,

$\tan \theta =\frac{y}{x} \\\\\tan \theta =\dfrac{2.169}{1.244}\\\\ \theta=\arctan \dfrac{2.169}{1.244}\\\\\\ \theta=1.05006$

Vanessa swept out approximately 1.05 radians since she started skiing.