Here's my correct answer.
The area of the shaded = the area of the sector - the area of the isosceles triangle.
Split the isosceles triangle in half, there will be 2 equivalent right triangles , where the radius is the hypotenuse. The measure of those angles are 15, 75 and 90 degrees.
Given hypotenuse = radius = 27.8 in
Sin(15) = opp./hypo
Opp = sin(15) * hypo = 0.2588 * 27.8 = 7.2 in
Now you know one leg = 7.2 in and hypo = 27.8
To find another leg,
a^2 = c^2 – b^2
a^2 = 27.8^2 – 7.2^2 = 772.84 – 51.84 = 721
a = 26.9
Area of 2 equal right triangles = area of the isosceles triangle = 26.9 x 7.2 = 193.68 = 193.7 in^2
Area of sector = (150 / 360) π r^2
= (150 / 360) (3.14) (27.8)^2
= 0.4 * (3.14) (772.84)
= 970.7 in^2
Area of shaded = 970.7 in^2 - 193.7 in^2= 777 in^2
Answer:
777 in^2
