Mathematics Question and Solution
Calculating angle x.
Let AB be 1 unit.
a = 9-20
a = 70°
a is angle ABH.
b = 180-10-70
b = 100°
(c/sin70) = (1/sin100)
c = 0.9541888941 units.
(d/sin10) = (1/sin100)
d = 0.1763269807 units.
sin20 = e/1
e = 0.3420201433 units
e is BH.
cos20 =f/1
f = 0.9396926208 units.
f is AH.
g = e-d
g = 0.3420201433-0.1763269807
g = 0.1656931626 units.
h = 180-20-30
h = 130°
(1/sin130) = (j/sin30)
j = 0.6527036447 units.
k = f-j
k = 0.9396926208-0.6527036447
k = 0.2869889761 units.
Therefore, the required angle x is;
tanx = g/k
tanx = (0.1656931626/0.2869889761)
x = atan(0.1656931626/0.2869889761)
x = 30°
Again, x is the required angle.
