Mathematics Question and Solution
Calculating Area Triangle AED.
Let x be CD.
Figuring an equilateral triangle OCD considering the strategic given two equal angles, 60°.
a = (x-8) units.
a is DE.
b = (x-10) units.
b is OA.
cos60 = c/8
c = 4 units.
c is BC.
d = (x-4) units.
d is OB.
Let AB = AE = y.
y² = (x-10)²+(x-4)²-2(x-4)(x-10)cos60
y² = x²-20x+100+x²-8x+16-(x²-14x+40)
y² = 2x²-28x+116-x²+14x-40
y² = x²-14x+76
y = √(x²-14x+76) units.
Therefore, calculating x, length CD.
√(x²-14x+76)² = 10²+(x-8)²-2*10(x-8)cos60
x²-14x+76 = 100+x²-16x+64-10x+80
-14x+76 = 100-16x+64-10x+80
26x-14x = 244-76
12x = 168
2x = 28
x = 14 units.
Again, x is length CD.
Recall.
a = (x-8) units.
And x = 14 units.
It implies;
a = 14-8
a = 6 units.
Again, a is length DE.
Therefore, the required area, area triangle AED is;
½*6*10sin60
= ¼*60√(3)
= 15√(3) square units.
