Let the three equal lengths be 1 unit.
it implies;
AB = BD = DE = 1 unit.
a² = 1²+1²-2*1*1cos100
a = 1.5320888862 units
a is AD.
c = ½(180-100)
c = 40°
c is angle ADB.
d = 180-40-40...
r, radius of the quarter circle is;
r = 8+6
r = 14 units.
a = 180-60
a = 120°
It implies;
Calculating x, observing Cosine Rule.
14² = 6²+x²-2*6*xcos120
196 = 36+x²+6x
x²+6x-160 = 0...
Sir Mike Ambrose is the author of the question.
y = 2^(x)
P coordinate is;
P(1, 2)
dy/dx = 2^(x)In2
For x = 1
dy/dx = 2In2
It implies;
Q coordinate is;
Q(0, (2-2In2))
Therefore;...
Calculating x.
a =4x-x
a = 3x
tanb = 3x/4x
b = atan(3/4)°
c = atan(4/3)°
d = ½(c)
d = 0.5atan(4/3)°
It implies
tan(0.5atan(4/3)) = 4/e
e = 4/(tan(0.5atan(4/3)))
e = 4/(0.5)
e = 8 units.
It...
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Let the three equal lengths be a.
Radius r of the semi circle is;
r = 5+4
r = 9 units.
5² = b²+a²-2abcos45
25 = b²+a²-√(2)ab --- (1).
9² = b²+a²-2abcos135
81 = b²+a²+√(2)ab --- (2).
Solving (1)...
Let the three equal lengths be 1 unit each.
a = 180-15-45
a = 120°
b = 180-120
b = 60°
It implies;
(c/sin45) = (1/sin15)
c = 2.7320508076 units
d² = 2.7320508076²+2²-2*2*2.7320508076cos60
d = 2...
a = 180-50-30
a = 100°
a is angle AED.
Let DE = 1 unit.
(1/sin30) = (b/sin100)
b = 1.969615506 units.
b is AD.
c = 180-80-50
c = 50°
c is angle CAD.
(1.969615506/sin80) = (d/sin50)
d = 1.5320888...
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a² = 11*11+10*10-2*11*10cos50
a = 8.92113926968 cm.
(8.92113926968/sin50) = (10/sinb)
b = 59.16920318624°
c = 180-50-59.16920318624
c = 70.83079681376°
d = 0.5a
d = 4.46056963484 cm.
e² = 4.460...
