AC = √(4²+4²)
AC = √(32)
AC = 4√(2) Units.
(4√(2))² = (4+r)²+r²
32 = 16+8r+r²+r²
2r²+8r-16 = 0
r²+4r-8 = 0
(r+2)² = 12
r = -2±2√(3)
r ≠ -2-2√(3) units.
r = (2√(3)-2) units.
a = r+4
a = (2+2√(3)) u...
r, radius of the inscribed circle is;
2(r/tan22.5) = 12√(2)
r = 6√(12)tan22.5
r = 3.51471862576 cm.
a = 12-3.51471862576
a = 8.48528137424 cm.
b = (8.48528137424-c) units.
c is the radius of the...
a² = 5²+2²
a = √(29) cm.
b² = 3²+2²
b = √(13) cm
c = atan(2/5)°
d = atan(1/3)°
e = atan(2/3)°
f = 90-c-d
f = 90-atan(2/5)-atan(1/3)
f = 49.76364169073°
g = atan(3)°
h = g-e
h = atan(3)-atan(2...
Let the height of the quadrilateral with parallel sides 7 cm and 9 cm be a.
b =√(a²+4) cm.
c = ½√(a²+4) cm.
d = √((½√(a²+4))²-1)
d = √(¼(a²+4)-1)
d = √(¼(a²))
d = ½(a) cm.
Considerin...
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Let the square side length be 2 units.
a² = 2
a = √(2) units.
a = 1.41421356237 units.
Calculating b.
c = atan(2)°
d = (180-atan(2))°
(1/sine) = (2/sin(180-atan(2))
e = 26.56505117708°
f = 180...
a² = 5²+12²
a = 13 cm.
a = AC = BD = diameter of the ascribed circle.
b = ½(13)
b = 6.5 cm.
b = OG = OE = radius of the ascribed circle.
c = atan(6/(6.5+2.5))
c = atan(6/9)
c = 33.69006752598°
c...
Let the square side be 2 units.
Area square is;
2²
= 4 square units.
Calculating Area A.
a² = 2²+1²-2*2*1cos45
a = √(5-2√(2)) units.
(√(5-2√(2))/sin45) = (2/sinb)
b = asin(√(2)/(√(5-2√(2))))°...
Notice!
BC+CD+DB = AD
Let BC = 1 unit.
(1/sin132) = (CD/sin12)
CD = 0.27977277603 units.
(1/sin132) = (BD/sin36)
BD = 0.79094307346 units.
Therefore;
AD = 0.79094307346+0.279772776...
Let a be the side of the square.
cos30 = b/8
b = 4√(3) cm.
sin30 = c/8
c = 4 cm.
a = b+12
a = (12+4√(3)) cm.
Area Square is;
a²
= (12+4√(3))²
= 358.27687752661 cm²
d² = 12²+4²-2*4*12cos30
d...
