Mathematics Question and Solution
Notice;
The figure is not drawn to scale.
Let BC be 1 unit.
(1/sin135) = (a/sin30)
a = 0.70710678119 units.
(1/sin135) = (b/sin15)
b = 0.36602540378 units.
Notice;
MB = NC, let it be c.
Therefore;
MN = (1-2c) units.
(AM)² = 0.36602540378²+c²-2*0.36602540378ccos30
(AM)² = 0.13397459621+c²-0.63397459621c --- (1)
(AN)² = 0.70710678119²+c²-2*0.70710678119ccos15
(AN)² = 0.5+c²-1.36602540379c --- (2)
Therefore;
Calculating c.
(MN)² = (AM)²+(AN)²
(1-2c)² = 0.13397459621+c²-0.63397459621c+0.5+c²-1.36602540379c
1-4c+4c² = 0.63397459621+2c²-2c
2c²-2c+0.36602540379 = 0
Solving the quadratic equation.
It implies;
c = 0.241181 units.
MN = 1-2(0.241181)
MN = 0.517638 units.
(AM)² = 0.36602540378²+0.241181²-2*0.36602540378*0.241181cos30
AM = 0.19809150382 units.
Therefore, the required ange x is;
(0.19809150382/sin30) = (0.241181/sinx)
x = 37.5°
