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...
Calculating AQ using similar plane shapes (triangle) rule.
12 = 6
6 = a cross multiply.
12a = 36
a = 3 cm.
Where a is AQ.
PQ = √(6²+3²)
PQ =√(45)
PQ = 3√(5) cm.
BQ = 12-3
BQ = 9 cm.
Calculati...
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E...
a = atan(2)°
b = 180-2a
b = (180-2atan(2))°
Where b is angle FBP.
Notice;
CQ = 5 cm.
Calculating FP using sine rule.
Let FP be c.
(c/sin(180-2atan(2))) = (5/sin(atan(2)))
c = 4.472135955 cm....
