(m+n)² = c²+b²-2bccosA --- (1).
h² = c²-m²
c² = h²+m² --- (2).
h² = b²-n²
b² = h²+n² --- (3).
Substituting (2) and (3) in (1).
(m+n)² = h²+m²+h²+n²-2bccosA
m²+2mn+n² = 2h²+m²+n²...
Let radius of the half circle be 2 units.
sin22.5 = d/2
d = 0.76536686473 units.
BZ = 2d
BZ = 1.53073372946 units.
e = 90-½(180-45)
e = 22.5°
cos22.5 = f/4
f = 3.69551813005 units....
Notice;
The diameter of the semicircle is 8 units.
Therefore radius is 4 units.
tan30 = a/2
a = ⅔(√(3)) units.
b = 3a
b = 2√(3) units.
c² = 2²+(⅔(√(3)))²
c = (4/√(3)) units.
d = (2/√(3))+c
d =...
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a² = 2*12²
a = 12√(2) cm.
Where a is AC = AE.
b = 180-45
b = 135°
Where b is angle EAB.
c² = (12√(2))²+12²-24*12√(2)cos135
c = 12√(5) cm.
Where c is BE.
(12√(5)/sin135) = (12√(2)/sind)
d = 26.565...
a = 90+60
a = 150°
Where a is angle ADF
b² = 12²+12²-2*12*12cos150
b = 23.18221983094 cm.
Where b is AF.
c = ½(180-150)
c = 15°
Where c is angle DAF = angle DFA.
d = 90-15
d = 75°
Where d is angl...
a² = 3²+4²
a = 5 cm.
Where a is AC.
b = atan(4/3)°
Where b is angle DAC.
c = 60+atan(4/3)
c = 113.13010235416°
Where c is angle EAC.
d² = 3²+5²-2*3*5cos113.13010235416
d = 6.76643256752 cm.
Where...
The radius of the circle is 6 cm.
a = atan(2)°
Where a is angle AOB = angle COE.
Angle BOE = 180-atan(2)
= 116.56505117708°
Angle OBE = ½(180-116.56505117708)
= 31.71747441146°
b =...
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We make teaching and learning Mathematics fun for learners, we expose the simplicit...
Let r = 1 units.
Let the ascribed half circle's radius be x.
Therefore;
a = (x-2) units.
b = ½(x-2) units.
c = x-b
c = x-½(x-2)
c = ½(x+2) units.
d = 2a
d = 2(x-2)
d = (2x-4) units.
Therefore...
