Mathematics Question and Solution
a² = 3²+4²
a = √(25)
a = 5 units.
3b+4b+5b = 3*4
12b = 12
b = 1 unit.
b is the radius of the inscribed circle.
tanc = 3/4
c = atan(¾)°
d = ½(180-atan(¾))
d = 71.5650511771°
tane = 4/3
e = atan(4/3)°
f = ½(180-atan(4/3))
f = 63.4349488229°
sin71.5650511771 = 1/g
g = 1.0540925534 units.
sin63.4349488229 = 1/h
h = 1.1180339888 units.
j = 90-71.5650511771
j = 18.4349488229°
k = 90-63.4349488229
k = 26.5650511771°
l = 180-26.5650511771-18.4349488229
l = 135°
Therefore, the required length, ? is;
?² = 1.0540925534²+1.1180339888²-2*1.0540925534*1.1180339888cos135
? = 2.0069324299 units.
? = 2 units.
