Mathematics Question and Solution
sin60 = 18/a
a = 20.7846096908 units.
tan60 = 18/b
b = 10.3923048454 units.
c+270+60+30+135 = 180(5-2)
c = 540-495
c = 45°
d² = 2(18²)
d = 18√(2) units.
d = 25.4558441227 units.
e = a+d
e = 20.7846096908+25.4558441227
e = 46.2404538135 units.
f = (85+z) units.
f is the required length x.
Therefore:
x = f = (85+z) units.
g = (46.2404538135+z) units.
tan60 = h/a
h = 20.7846096908tan60
h = 36 units.
j = (25.4558441227+z) units.
j is the required length y.
y = j = (25.4558441227+z) units.
k = f-h
k = (85+z)-36
k = (49+z) units.
Observing the side length ratios of similar right-angled triangles.
20.7846096908 - (25.4558441227+z)
36 - (49+z)
Cross Multiply.
20.7846096908(49+z) = 36(25.4558441227+z)
20.7846096908z+1018.4458748492 = 36z+916.4103884172
15.2153903092z = 102.035486432
z = 6.7060709163 units.
Therefore, required length x is;
x = f = (85+z)
And z = 6.7060709163 units.
x = 85+6.7060709163
x = 91.7060709163 units.
Therefore, required length y is;
y = j = (25.4558441227+z)
And z = 6.7060709163 units.
y = 25.4558441227+6.7060709163
y = 32.161915039 units.
