Diagonals of pentagon

Calculate the diagonal length of the regular pentagon:
a) inscribed in a circle of radius 12dm;
b) a circumscribed circle with a radius of 12dm.

Correct answer:

u1 =  22.8254 dm
u2 =  28.2137 dm

Step-by-step explanation:

r1=12 cm A=360/(2 5)=36   sin A = a1/2 : r1  a1=2 r1 sinA=2 r1 sin36° =2 12 sin36° =2 12 0.587785=14.10685 cm  u1=a1/2 (1+5)=14.1068/2 (1+5)=22.8254 dm
r2=12 cm  tan A = a2/2 : r2  a2=2 r2 tanA=2 r2 tan36° =2 12 tan36° =2 12 0.726543=17.43702 cm  u2=a2/2 (1+5)=17.437/2 (1+5)=28.2137 dm

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