Considering similar plane shapes (triangle) ratios;
10 = y
(16+x) = x
Cross multiply and making y the subject of the formula.
y = 10x/(16+x) ----- (1)
And;
24+½(xy) = ½)10x) ----- (2)
Su...
Calculating BC.
(BC/sin30) = (12/sin75)
BC = 6.21165708246 cm.
Calculating EF.
(6.21165708246/sin75) = (EF/sin30)
EF = 3.21539030917 cm.
Angle FEG is;
360-2(75)-60
= 360-210
= 150°
It implies;...
Let the radius of the circle be r.
Calculating r.
√(r²-4)+√(r²-1) = 3
r²-4 = (3-√(r²-1))²
r²-4 = 9-6√(r²-1)+r²-1
6√(r²-1) = 12
√(r²-1) = 2
r = √(5) units.
BC = √(3²+4²)
BC = 5 cm.
tana = (4/3)
a = atan(4/3)°
tan(½(atan(4/3))) = AF/3
AF = 3tan(½(atan(4/3)))
AF = 1.5 cm.
b = 90-½(atan(4/3))
b = 63.43494882292°
Where b is angle AFE.
sin63.43494882292...
Screenshot of yesterday's teaching and learning activities with very talented, Mathematician Adesuwa, she is a year 5 pupil.
Educator:
Mr. Daniel
Adesuwa is smart and clever.
Calculating r, radius of the circle.
r² = (r-3)²+4²
r² = r²-6r+9+16
6r = 25
r = (25/6) units.
a = r-3
a = (25/6)-3
a = (25-18)/6
a = (7/6) units.
tanb = (7/6)/4
b = atan(7/24)°
c = 180-b
c = (18...
Let r be the radius of the semi circle.
Calculating r.
√(r²-49)+√(r²-36) = 12
r²-49 = (12-√(r²-36))²
r²-49 = 144-24√(r²-36)+r²-36
24√(r²-36) = 144+13
24√(r²-36) = 157
r²-36 = (157/24)²
r² = (157/2...
Angle DAG = 60-45
= 15°
Angle DAG = Angle DCF
= 15°
Angle CDF = 90-15 = 75°
Angle ADG = 90-75 = 15°
It implies;
Triangle ADG is an isosceles.
Calculating DG.
cos15 = 6/(DG)
DG = 6/cos15
D...
tanx = 2/a
a = 2/tanx ----- (1).
b = a+2
b = (2/tanx) + 2 ----- (2).
Notice;
a = the short adjacent length of the right-angled triangle.
b = the long adjacent length of the right-angle...
Let the height of the triangle be a.
Let angle alpha be b.
tanb = 3/a ----- (1)
tan2b = 8/a ----- (2)
And tan2b = 2tanb/(1-tan²b)
Therefore;
2tanb/(1-tan²b) = 8/a ----- (3)
Substituting (1) in...
