Mathematics Question and Solution
Kindly move the question left/right one time to review the analysis of the question (plane shape).
Thank you nicely.
Calculating R, radius of the quarter circle.
a = 3+4
a = 7 units.
b² = 2(4)²
b = 4√(2) units.
c = R-b
c = (R-4√(2)) units.
d = 180-45
d = 135°
R is;
Observing cosine rule.
R² = 7²+(R-4√(2))²-2*7(R-4√(2))cos135
R² = 49+R²-8√(2)R+32+7√(2)(R-4√(2))
8√(2)R = 81+7√(2)R-56
√(2)R = 25
R = ½(25√(2)) units.
R = 17.6776695297 units.
Or
e² = 3²+4²
e = √(25)
e = 5 units.
tanf = 3/4
f = atan(3/4)°
g = 45+f
g = (45+atan(3/4))°
h = 180-2g
h = (180-2(45+atan(3/4)))°
h = 16.2602047083°
Calculating R, observing cosine rule.
5² = 2R²-2R²cos16.2602047083
25 = 0.08R²
8R² = 2500
R² = (2500/8)
R = √(2500/8)
R = 50/(2√(2))
R = ½(25√(2)) units.
R = 17.6776695297 units.
