Calculating r, radius of the circle.
r² = (r-3)²+4²
r² = r²-6r+9+16
6r = 25
r = (25/6) units.
a = r-3
a = (25/6)-3
a = (25-18)/6
a = (7/6) units.
tanb = (7/6)/4
b = atan(7/24)°
c = 180-b
c = (18...
Let r be the radius of the semi circle.
Calculating r.
√(r²-49)+√(r²-36) = 12
r²-49 = (12-√(r²-36))²
r²-49 = 144-24√(r²-36)+r²-36
24√(r²-36) = 144+13
24√(r²-36) = 157
r²-36 = (157/24)²
r² = (157/2...
Angle DAG = 60-45
= 15°
Angle DAG = Angle DCF
= 15°
Angle CDF = 90-15 = 75°
Angle ADG = 90-75 = 15°
It implies;
Triangle ADG is an isosceles.
Calculating DG.
cos15 = 6/(DG)
DG = 6/cos15
D...
tanx = 2/a
a = 2/tanx ----- (1).
b = a+2
b = (2/tanx) + 2 ----- (2).
Notice;
a = the short adjacent length of the right-angled triangle.
b = the long adjacent length of the right-angle...
Let the height of the triangle be a.
Let angle alpha be b.
tanb = 3/a ----- (1)
tan2b = 8/a ----- (2)
And tan2b = 2tanb/(1-tan²b)
Therefore;
2tanb/(1-tan²b) = 8/a ----- (3)
Substituting (1) in...
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Please, move a step right to view the analyzed figure.
Notice;
ABC triangle is Isosceles.
a² = 3²-2²
a = √(5) units.
Where a is AD.
tanb = ½(√(5))°
b = atan(½(√(5)))°
b = 48.18968510422...
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Let the ascribed quarter circle be 2 units.
2a² = 2²
a² = 2
a = √(2) units.
b = (2-√(2)) units.
c² = (√(2))²+(2-√(2))²
c² = 2+4-4√(2)+2
c² = 8-4√(2)
c = √(8-4√(2)) units.
d² = √(8-4√(2))²-√(2)²...
Let the square side be 2 units.
a = √(2²+1²)
a = √(5) units.
b = atan(2)°
c = atan(½)°
d² = 8-8cos150
d = 3.86370330516 units.
e = 0.5d
e = 1.93185165258 units.
f = 90-15-atan(½)
f = 48.434948...
