Sir Mike Ambrose is the author of the question.
a = ½√(2²+2²)
a = √(2) units.
b² = (√(2))²+(√(2))²
b = 2 units.
c² = 3²+1²
c = √(10) units.
d = (135+atan(⅓))°
e² = 10+2-2√(20)cos(135+atan(⅓))
e...
Sir Mike Ambrose is the author of the question.
(a) Calculating Length Blue ÷ AB.
Let AB be 1 unit.
a² = 1²+1²-2cos108
a = 1.61803398875 units.
b² = 1.61803398875²-0.5²
b = 1.53884176859 units....
Sir Mike Ambrose is the author of the question.
Let the small regular hexagon be 2 units.
a² = 2²+1²-2*2*1cos120
a = 2.64575131106 units.
Where a is the side length of the big regular hexagon.
(2...
Let the big square side length be 1 unit.
tan15 = a/1
a = 0.26794919243 units.
b = 1-0.26794919243
b = 0.73205080757 units.
sin75 = c/0.73205080757
c = 0.70710678119 units.
c is the side length...
Let AB be 2 units.
tan(atan½) = a/1
a = ½ unit.
b = (atan(⅔))°
tan(atan⅔) = c/1
c = ⅔ units.
d = (180-atan⅔-atan2)°
(e/sin(atan2)) = (1/sin (180-atan⅔-atan2))
e = ¼√(13) unit.
It implies;
Are...
Let the side length of the regular pentagon be 1 unit.
a² = 2-2cos108
a = 1.61803398875 units.
a is the side length of the square.
sin18 = b/1
b = 0.30901699437 units.
cos18 = c/1
c = 0.951056516...
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Let AC be 2 units.
a = √(2²+2²)
a = √(8) units.
a = 2√(2) units.
Let the side length of the inscribed regular hexagon be b.
c² = 2b²-2b²cos120
c = √(3)b units.
d = 0.5b units.
e = √(2) units....
a² =10²-6²
a = 8 cm.
tanb = 3/4
b = atan(3/4)°
(3/4) = c/10
c = ½(15) cm.
c = 7.5 cm.
sin(atan(3/4)) = d/8
d = 4.8 cm.
e = 7.5-4.8
e = 2.7 cm.
(3/4) = 2.7/f
f = 3.6 cm.
g² = 2.7²+3.6²
g = 4.5...
Sir Mike Ambrose is the author of the question.
Let alpha be x.
tanx = 10/a --- (1)
tan2x = a/30 --- (2)
From (2)
a = 30tan2x --- (3)
Sub. (3) in (1)
tanx = 10/30tan2x
tanxtan2x = ⅓
tanx(2tanx/(1...
