Mathematics Question and Solution
Calculating x.
7² = x²+5²+2*5*xcosa
49 = x²+25+10xcosa
24 = x²+10xcosa
10xcosa = 24-x²
cosa = (24-x²)/(10x) --- (1).
b = (x+5) units.
7² = x²+(x+5)²-2x(x+5)cosa
49 = x²+x²+10x+25-(2x²+10x)cosa
24 = 2x²+10x-(2x²+10x)cosa --- (2).
Substituting (1) in (2).
24 = 2x²+10x-(2x²+10x)cosa
And cosa = (24-x²)/(10x)
24 = 2x²+10x-(2x²+10x)(24-x²)/(10x)
240= 20x²+100x-(2x+10)(24-x²)
240 = 20x²+100x-(48x-2x³+240-10x²)
240 = 20x²+100x-48x+2x³-240+10x²
480 = 2x²+30x²+52x
x³+15x²+26x-240= 0
It implies;
x = 3 units.
x is the required side length.
