Find the area of the segment shaded in blue in the figure of

Find the area of the segment (shaded in blue in the figure) of a circle whose radius is 3 feet, formed by a central angle of 50degree. The area of the segment is approximately square feet. (Do not round until the final answer. Then round to two decimal places as needed.)

Solution

Area of triangle with sides radius and angle = 50 deg is (1/2)*3*3sin50

= 3.447 sqft

Area of sector with central angle 50 deg = (50/360)*pi*3^2 = 3.926 sqft

So, Area of segment = Area of sector with central angle 50 deg - Area of triangle with sides radius and angle

= 3.926 - 3.447

=0.48 sqft