Mathematics Question and Solution
Calculating angle a.
Let the length of the ascribed rectangle be 2 units.
Therefore it's width is 1 unit.
b² = 2²+1²
b = √(5) units.
b is the diagonal of the ascribed rectangle.
tanc = 1/2
c = atan(½)°
tand = 1/0.5
d = atan(2)°
e = 2d
e = 2atan(2)°
f = ½(180-2atan(2)°)
f = (90-atan(2))°
g² = 2(0.5)²-2(0.5)²cos(2atan(2))
g = 0.894427191 units.
h = 90-f-c
h = 90-(90-atan(2))-atan(½)
h = (atan(2)-atan(½))°
h = 36.8698976458°
j² = 0.894427191²+√(5)²-2*0.894427191√(5)cos36.8698976458
j = 1.61245154966 units.
Therefore, angle a is;
(1.61245154966/sin36.8698976458) = (0.894427191/sina)
sina = 0.33282011773
a = asin(0.33282011773)
a = 19.4400348279°
a ≈ 19.44° to 2 decimal places.
