a = 2+3
a = 5 units.
5² = 3²+b²
b = √(25-9)
b = 4 units.
c = 2+4
c = 6 units.
Let d be the radius of the ascribed semi circle.
e = c-d
e = (6-d) units.
d² = f²+3²
f = √(d²-9) u...
Sir Mike Ambrose is the author of the question.
Let the two equal length of the inscribed isosceles triangle (red area) be 2 unit.
Therefore;
Area blue will be;
Area triangle with lengt...
Calculating Yellow Shaded Area.
Radius, r of the inscribed circle is;
Cos30=r/4
r = 2√(3) in.
Length AD = DB = 2 in.
Or
Length AD = DB is;
= √(4²-(2√(3))²)
= √(16-12)
= √(4) = 2...
Calculating the radius of each of the inscribed circles.
The biggest inscribed circle radius, R is;
3.3R+2.73R+1.84R=(2.73x1.84)
7.87R = (2.73x1.84)
R = 0.63827191868 m.
The bigger inscr...
Let the side length of the square be 1 unit.
Calculating angle x.
a = 180-60-70
a = 50°
(1/sin50) = (b/sin60)
b = 1.1305158748 units.
c² = 2(1)²
c = √(2) units.
c is the diagonal of...
Let to theta be x.
Let beta be y.
a = 90+60
a = 150°
b = ½(180-150)
b = 15°
c = 90-15
c = 75°
Therefore, x is;
x = c
x = 75° (vertically opposite angles are equal).
Calculat...
Notice!
The angles are exterior.
The sum of exterior angles is 360°
The exterior angles are arranged in order (clockwise).
Calculating x.
It implies;
x+2x+86+70 = 360
3x = 360-156...
Notice!
Radius of the inscribed half circle is 4 units.
tana = 4/8
a = atan(½)°
b = 2a
b = 2atan(½)°
c = 90-b
c = (90-2atan(½))°
tan(90-2atan(½)) = d/8
d = 6 units.
Therefore, a...
Calculating x.
a²+x² = 1
a = √(1-x²) units.
b = (1+x) units.
Observing similar plane shape (right-angled) side length ratios.
1 - √(1-x²)
(1+x) - x
Cross Multiply.
x = √(1-x²)(1...
Let AB, the side length of the square be 1 unit.
a² = 1²+1²
a = √(2) units.
b²+1² = c²
c = √(b²+1) units.
b is the radius of the inscribed circle.
d² = 2b²
d = √(2)b units.
It impli...
