Let a be the side length of the regular hexagon.
3² = 1²+a²-2acosb
2acosb = a²-8
cosb = (a²-8)/(2a) --- (1).
c²+(a²-8)² = (2a)²
c² = 4a²-(a⁴-16a²+64)
c = √(-a⁴+20a²-64) units.
sinb = c...
Let the radius of the semi circle be 3 units.
Calculating area Red.
Area red will be;
2(area triangle of two length 3 units and 1 unit, and angle (cos–¹(⅓)), angle they form) + area sector...
a = 180-75-27
a = 78°
b = 1+½(√(5)+1)
b = 2.61803398875 units.
(2.61803398875/sin78) = (c/sin27)
c = 1.21511575349 units.
sin75 = d/1.21511575349
d = 1.17371168822 units.
cos75 = e...
Sir Mike Ambrose is the author of the question.
Area W to 3 decimal places is;
Area triangle of two length 5 units and 7.5 units, and angle 86.4166783015° - Area triangle of two length 5 units...
Sir Mike Ambrose is the author of the question.
Let the length of the inscribed rectangle be 2 units.
Let the width of the inscribed rectangle be √(3) units.
Therefore the single side length...
Let r be the radius of the quarter circle.
Let x be the interior angle facing 1 cm.
a = (x+45)°
a is alternate to y, the angle formed by the meet point of r and 2 cm at the circumference of...
Let a be the radius of the inscribed half circle.
b²+8² = (2a)²
b = √(4a²-64) units.
It implies;
Calculating a.
2a ~ 8
a ~ √(4a²-64)
Cross Multiply.
8a = 2a√(4a²-64)
4 = √(4a²-...
Let a be the radius of the red inscribed circle.
b = (4-a) units.
tan30 = a/b
⅓√(3) = a/(4-a)
3a = 4√(3)-√(3)a
(3+√(3))a = 4√(3)
a = 4√(3)/(3+√(3))
a = ⅙(12√(3)-12)
a = (2√(3)-2) units....
Let a be the radius of the circle.
c = (a-1) units.
Calculating a.
7² = a²+(a-1)²-2a(a-1)cosb
49 = a²+a²-2a+1-(2a²-2a)cosb
48 = 2a²-2a-(2a²-2a)cosb
(2a²-2a)cosb = 2a²-2a-48 --- (1)....
Let a be the radius of the inscribed circle.
b² = 2(10)²
b = 10√(2) cm.
b is the diagonal of the square.
10²+a² = c²
c = √(100+a²) cm.
d = b-c
d = (10√(2)-√(100+a²)) cm.
Calculating a.
2a² = (1...
