Mathematics Question and Solution
Mazana Job Shared The Questions.
Number 1.
a = 180-30-45
a = 105°
It implies;
(4/sin105) = (b/sin30)
b = 2.0705523608 units.
c = 45+90
c = 135°
Therefore, the required length, ? is;
?² = 4²+2.0705523608²-2*4*2.0705523608cos135
? = 5.6568542495 units.
Number 2.
Calculating yellow area.
Let a be the radius of the inscribed quarter circle, and also, the side length of the ascribed square.
tanb = a/(0.5a)
b = atan(2)°
sin(atan(2)) = c/4
c = 3.577708764 units.
cos(atan(2)) = d/4
d = 1.788854382 units.
e = (a-1.788854382) units.
Therefore, a is
a² = 3.577708764²+(a-1.788854382)²
a² = 12.8+a²-3.577708764a+3.2
3.577708764a = 16
a = (16/3.577708764)
a = 4.472135955 units.
Again, a is the radius of the inscribed quarter circle, and also, the side length of the ascribed square.
It implies, area yellow inscribed rectangle is;
a*d
= 4.472135955*1.788854382
= 8 square units.
