Let r be the radius of the inscribed semi circle.
Calculating r.
r² = (r-4)²+(r-8)²
r² = r²-8r+16+r²-16r+64
r²-24r+80 = 0
It implies;
r ≠ 4 cm.
r = 20 cm.
a² = 20²+16²
a = 4√(41) cm.
(4/sinb) =...
Area Shaded exactly in square units as a single fraction is;
Area triangle with height 6√(3) units and base 6 units - Area triangle with height 2√(3) units and base 2 units - Area sector with radiu...
Let the side of the equilateral triangle be 2 units.
Let the side of the square be a.
Calculating a.
tan60 = a/1
a = √(3) units.
Area square is;
a²
= √(3)²
= 3 square units.
Calculating area...
Let the shortest length of the composite plane shape be 1 unit.
(1/sin12) = (a/sin153)
a = 2.18357369878 units.
(2.18357369878/sin27) = (b/sin99)
b = 4.75051853365 units.
c² = 4.75051853365+1-2*4...
Let the a side length of the yellow regular triangle be 2 units.
Therefore, a side length of the regular pentagon is 2 units.
Area Yellow is;
0.5*2*2sin60
= 2sin60
= √(3) square units.
= 1.732050...
Notice;
GH = 8 units.
Calculating the side length of the regular pentagon.
a = 108-90
a = 18°
a is angle EFG.
b = 180-108-18
b = 54°
b is angle EGF.
(8/sin108) = (c/sin18)
c = 2.59935756986 uni...
Our certified, experienced, resilient, productive and committed Math Educators will be glad to be at your service.
We make teaching and learning Mathematics fun for learners, we expose the simplicit...
Let the adjacent base and adjacent height of the triangle be 3 units each.
a² = 2*3²
a = 3√(2) units.
b = ⅓(a)
b = ⅓(3√(2))
b = √(2) units.
c² = 2+9-6√(2)cos45
c = √(5) units.
(√(5)/sin45) = (√...
Let AB = 1 unit.
a² = 2-2cos108
a = 1.61803398875 units.
a is AD.
b = 108-36-18
b = 54°
b is angle DAF.
c = 108-36-30
c = 42°
c is angle ADF.
d = 180-54-42
d = 84°
d is angle AFD.
(1.6180339887...
Let the side length of the regular pentagon be 2 units.
a² = 2²-1²
a = √(3) units.
b² = 5-4cos108
b = 2.49721204096 units.
(2.49721204096/sin108) = (2/sinc)
c = 49.61382244056°
d = 90-c
d = 40.3...
