Mathematics Question and Solution
Notice!
Radius, a of the inscribed circle is 4 units.
Radius, b of the inscribed semi circle is 7 units.
3²+4² = c²
c = √(25)
c = 5 units.
d² = 5²+4²
d = √(41) units.
tane = 3/4
e = atan(3/4)°
f = 90+e
f = (90+atan(3/4))°
g² = 2(4)²-2*4²cos(90+atan(3/4))
g = 7.155417528 units.
h = ½(180-(90+atan(3/4)))
h = 26.5650511771°
j = 90-h
j = 63.4349488229°
k = 180-2j
k = 53.1301023542°
It implies;
Length x is;
tan53.1301023542 = 7/x
x = 5¼ units.
It implies;
Length y is;
tan53.1301023542 = y/7
y = 9⅓ units.
Therefore; x+y is;
= 5¼+9⅓
= (21/4)+(28/3)
= (63+112)/12
= 175/12 units.
= 14.5833333333 units.
