Mathematics Question and Solution
Calculating r, radius of the half circle.
Let the two equal lengths be a each.
Therefore;
r = 2a units.
Calculating a.
(2a)² = a²+9²-2a*9cosb
3a² = 81+18acosb
cosb = (3a²-81)/(18a)
cosb = (a²-27)/(6a) --- (1).
cosb = 3/a --- (2).
Equating (1) and (2).
(a²-27)/(6a) = 3/a
a²-27 = 18
a² = 45
a = √(45)
a = 3√(5) units.
Therefore r, radius of the half circle is ;
Recall.
r = 2a
And a = 3√(5) units.
r = 2(3√(5))
r = 6√(5) units.
r = 13.416407865 units.
