We want to find the area of the shaded portion of the figure below. The considered region is sector of a circle, which is the region bounded by an arc of the circle and the two radii to the arc's endpoints.
We know that the radius of the circle is 15 inches. We need to find the measure of the corresponding arc. Recall that the measure of an arc is the same as the measure of its corresponding central angle. Since the measure of a full turn is 360^(∘), to find the measure of our central angle we need to find the difference between 360^(∘) and the given angle 60^(∘).
360 ^(∘) - 60 ^(∘) = 300 ^(∘)
The measure of the central angle of our region is 300^(∘). Therefore, the measure of the arc is also 300^(∘). We have all the information we need to use the formula to find the area of sector.
