tana = 3/4
a = atan(3/4)
b² = 3²+4²
b = 5 units.
cos(atan(3/4)) = 1/c
c = 1.25 units.
c = (5/4) units.
sin(atan(3/4)) = 1/d
d = 1.6666666667 units.
d = (5/3) units.
e = b-c-d
e =...
Calculating angle x.
Let BC be 2 units.
a = 180-70-40
a = 70°
a is angle ACB.
cos70 = 1/b
b = 2.9238044002 units.
b is AB.
c = 180-80-50
c = 50°
c is angle ADC.
d = ½(b)
d = 1...
Sir Mike Ambrose is the author of the question.
Let the side length of the regular hexagon be 1 unit.
Therefore;
Area green is;
Area regular hexagon with side 1 unit + Area regular pentag...
Calculating radius of the quarter circle.
Let a be the radius of the quarter circle.
b = ½(DE)
b = 2√(2) units.
c²+(2√(2))² = a²
c² = a²-8
c = √(a²-8) units.
d = c-BE
d = (√(a²-8)-5)...
Calculating r.
a = (2+r) units.
b = (1+r) units.
c = r+r
c = 2r units.
It implies;
(2r)² = (1+r)²+(2+r)²-2(1+r)(2+r)cos60
4r² = 1+2r+r²+4+4r+r²-(2+3r+r²)
4r² = 2r²+6r+5-2-3r-r²
3...
Let x be 2 units.
Therefore;
Area square is;
8²
= 64 square units.
Calculating area rectangle.
The length is;
√(8²+6²) + 2cos(atan(4/3))
= 10+(6/5)
= 56/5 units.
The width i...
Area yellow is;
Area triangle with two side (6√(65)/7) cm and 7.95918367347 cm, and angle acos(7/√(65))°
= ½*(6√(65)/7)*7.95918367347sin(acos(7/√(65)))
= 13.6443148688 cm²
Area blue is;...
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the regular pentagon.
b = ⅙*180(6-2)
b = 120°
b is the single interior angle of the regular hexagon.
c+90+(180-30)+2(108) = 180(5...
Sir Mike Ambrose is the author of the question.
Area orange exactly in its decimal form is;
Half area square with side 12 units - Area triangle with height 12 units and base 12tan15 units - Are...
Let a be the radius of the inscribed blue circle.
b = (24-a) units.
c = ½(24)
c = 12 units.
Therefore, Calculating a.
a²+12² = (24-a)²
a²+144 = 576-48a+a²
48a = 432
a = 9 units.
Ag...
