Mathematics Question and Solution
Let x be the radius of the sector.
b = (x-1) units.
c = x+b
c = x+(x-1)
c = (2x-1) units.
Therefore;
5*3 = (2x-1)*1
15 = 2x-1
2x = 16
x = 8 units.
Again, a is the radius of the sector.
Recall.
b = (x-1)
And x = 8 units.
b = 8-1
b = 7 units.
Calculating angle a.
8² = 7²+5²-2*7*5cosa
64 = 49+25-70cosa
70cosa = 74-64
cosa = 10/70
cosa = 1/7
Calculating sina.
Notice.
At cosa = 1/7
1 is adjacent.
7 is hypotenuse.
Calculating opposite, let it be d.
d²+1² = 7²
d² = 49-1
d = √(48)
d = 4√(3) units.
Therefore;
sina = d/7
sina = ⅐(4√(3))
Calculating length of arc of the sector.
Notice.
The triangle inscribed the second is equilateral.
Let e be the length of the sector.
e = (60π*2*8)/360
e = ⅙(2*8π)
e = ⅓(8π) units.
