Let r be 1 unit.
Calculating R.
(R+1)² = x²+(R-1)²
Calculating x.
x² = R²+2R+1-R²+2R-1
x = √(4R)
x = 2√(R) units.
It implies;
(2R)² = (2√(R))²+2²
4R² = 4R+4
R²-R-1= 0
Solving the quadratic equ...
Let the two congruent lengths be 1 unit.
(1/sin50) = (a/sin80)
a = 1.28557521937 units.
(1.28557521937/sin110) = (b/sin60)
b = 0.46791111376 units.
(1/sin70) = (c/sin80)
c = 1.04801052092 units....
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The side length of the congruent Hexagons is 2 unit.
Area hexagon is;
(6*2²)/(4tan30)
= 6√(3)) square units.
a² = 8-8cos30
a = √(8-4√(3)) unit.
Area ABC is;
½(√(8-4√(3)))²sin60
= (2√(3)-3) squa...
25 = 49+64-14*8cosa
112cosa = 113-25
a = acos(88/112)
a = 38.21321070174°
a = Angle ACB.
5b+7b+8b = 56sin38.21321070174
b = (56sin38.21321070174)/20
b = √(3) cm
b = 1.73205080757 cm.
b = radius o...
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Let the two equal lengths be 1 unit.
(a) Calculating Theta exactly.
Let theta be x.
Calculating x.
x = ½(90-54)
x = ½(36)
x = 18°
sin18 = a/1
a = 0.30901699437 unit.
b = 90-18
b = 72°
sin72 =...
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Radius of the semi circle is 5 units.
Calculating r, radius of the inscribed circle.
(5-r)² = 3²+r²
25-10r+r² = 9+r²
10r = 16
r = ⅕(8) units.
a = 3-r
a = ⅕(7) units.
b² = 5²-a²
b = ⅕(24) units....
AE = CF = (12√(2)-12) cm.
AE = CF = 4.97056274848 cm.
EF = 12√(2)-2(4.97056274848)
EF = 7.02943725152 cm.
sin60 = a/7.02943725152
a = 6.08767123412 cm.
a = height of triangle EFG.
It implies;
L...
