Mathematics Question and Solution
Calculating angle x.
a = 180-2(58)-48
a = 180-116-48
a = 180-164
a = 16°
a is angle BAD.
Let 1 unit be the let AB equal length AC.
(a')² = 2-2cos(a+48)
a' = √(2-2cos64)
a' = 1.05983852847 units.
a' is length BC.
b = 180-48-58-30
b = 180-136
b = 44°
b is angle ADC.
(c/sin48) = (1/sin44)
c = 1.06979899341 units
c is length CD.
(d/sin(58+30)) = (1/sin44)
d = 1.43867960068 units.
d is length AD.
e² = 1+1.43867960068²-2*1.43867960068cos16
e = 0.55127471164 units.
e is length BD.
Therefore, the required angle x, angle ADB is;
(0.55127471164/sin16) = (1/sinx)
sinx = 0.5
x = 30°
