Mathematics Question and Solution
cos30 = a/10
a = 5√(3) units.
sin30 = b/10
b = 5 units.
cos40 = c/10
c = 7.6604444312 units.
sin40 = d/10
d = 6.4278760969 units.
e = 180-30-40
e = 110°
(10/sin110) = (f/sin30)
f = 5.3208888624 units.
g = 90-30
g = 60°
h = 90-40
h = 50°
j = 180-50-50
j = 80°
k = 180-60-80
k = 40°
(10/sin110) = (l/sin40)
l = 6.8404028665 units.
m = a-l
m = 5√(3)-6.8404028665
m = 1.8198511713 units.
n = c-f
n = 7.6604444312-5.3208888624
n = 2.3395555688 units.
Notice!
Radius of the half circle, o is;
o = ½(10)
o = 5 units.
Therefore;
Shaded Area is;
Area triangle with height 1.8198511713 units and base 2.3395555688sin110 units + Area sector with radius 5 units and angle 40° - Area triangle with height 5 units and base 5sin40°
= (0.5*1.8198511713*2.3395555688sin110)+(40π*5*5÷360)-(0.5*5*5sin40)
= 2.0004378274+8.72664626-8.0348451211
= 2.6922389663 square units.
