Area Triangle is;
16tan(sin–¹(1/3))
= 5.65685424949 square units.
Or
sina = ⅓
a = asin(⅓)°
tana = b/4
b = 4tan(asin(⅓)) units.
c = 2b
c = 8tan(asin(⅓)) units.
Therefore, area triangle is;...
Calculating angle a.
Let the length of the ascribed rectangle be 2 units.
Therefore it's width is 1 unit.
b² = 2²+1²
b = √(5) units.
b is the diagonal of the ascribed rectangle.
tanc...
Calculating x.
Notice.
The composite plane shape is drawn to scale.
2(60+x)+x = 180
120+2x+x = 180
3x = 60
x = 20°
Or
(60-x)+2(60+10) = 180
60-x+140 = 18
200-x = 180...
It will be;
Let the single side length of the regular heptagon be 5 units.
Therefore;
(1/x) + (1/y) will be;
(1÷(√(50-50cos129))) + (1÷(5+10cos51))
= 0.19934168501≈ 0.2 units.
Sir Mike Ambrose is the author of the question.
Let the side length of the introduced equilateral triangle inscribing the circle be 2 units.
Calculating r, radius of the circle.
cos30 = 1/r...
Sir Mike Ambrose is the author of the question.
Let the ascribed circle's radius be 1 unit.
Area ascribed circle is;
π(1)²
= π square units.
Calculating shaded area.
Notice.
The side...
Sir Mike Ambrose is the author of the question.
Let AB be 2 units.
Area ABCD is;
2²
= 4 square units.
Let the side length of the ascribed square be x.
Calculating x.
a = (x-2) unit...
Let the two equal smaller inscribed circle radius be r.
Let the radius of the smallest inscribed circle be q.
The radius is the biggest inscribed circle is 0.5 units.
Therefore;
x+2r=0....
Length EF will be;
√(49+50-70√(2)cos(tan-¹(¾)+45))
EF = √(85) units.
Notice.
r, radius of the ascribed half circle is 5 units.
Calculating the area of the inscribed red circle.
Let it's radius be x.
Calculating x.
a = (5-x) units.
tan15 = x/b
b =...
