Mathematics Question and Solution
Notice.
The composite plane shape consist of two regular plane shapes, a square and an equilateral triangle.
Let the four congruent units of the square be 1 each.
It implies a, the square side is;
a = 3 units.
b² = 3²+1²
b² = 9+1
b = √(10) units.
b is a side length of the regular triangle (equilateral triangle).
tanc= 1/3
c = atan(⅓)°
d = 60-c
d = (60-atan(⅓))°
e = 90+d
e = 90+(60-atan(⅓))
e = (150-atan(⅓))°
e = 131.5650511771°
It implies;
f² = 3²+√(10)²-2*3√(10)cos131.5650511771
f = 5.6203609553 units.
(5.6203609553/sin131.5650511771) = (√(10)/sing)
g = 24.896090639°
tan24.896090639 = h/3
h = 1.3923048454 units.
cos24.896090639 = 3/i
i = 3.3073422536 units.
j = 3-1.3923048454-1
j = 0.6076951546 units.
k = 5.6203609553-3.3073422536
k = 2.3130187017 units.
l = 90-24.896090639
l = 65.103909361°
It implies;
m² = 0.6076951546²+2.3130187017-2*0.6076951546*2.3130187017cos65.103909361
m = 2.1297648661 units.
Therefore, n, the required angle is,
(2.1297648661/sin65.103909361) = (0.6076951546/sinn)
sinn = 0.2588190451
n = asin(0.2588190451)
n = 15°
Again, n, 15° is the required angle.
