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junior college 2 | H2 Maths
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How do I represent A in alpha?
Date Posted: 3 years ago
Views: 570
Left triangle :
Using sine rule,
(a/2) / sin(120°- α) = B / sin60°
a / 2sin(120° - α) = 2B / √3
2B = a√3 / 2sin(120° - α)
B = a√3 / 4sin(120° - α)
B = a√3 / 4(sin120° cos α - cos120° sin α)
B = a√3 / 4(√3/2 cos α - (-½ sin α) )
B = a√3 / 2(√3 cos α + sin α)
Area of A → formula ½ab sin c
= ½(a/2)(B) sin α
= (a/4) (a√3 / 2(√3 cos α + sin α) ) sin α
= a²√3 sin α / 8(√3 cos α + sin α)
Using sine rule,
(a/2) / sin(120°- α) = B / sin60°
a / 2sin(120° - α) = 2B / √3
2B = a√3 / 2sin(120° - α)
B = a√3 / 4sin(120° - α)
B = a√3 / 4(sin120° cos α - cos120° sin α)
B = a√3 / 4(√3/2 cos α - (-½ sin α) )
B = a√3 / 2(√3 cos α + sin α)
Area of A → formula ½ab sin c
= ½(a/2)(B) sin α
= (a/4) (a√3 / 2(√3 cos α + sin α) ) sin α
= a²√3 sin α / 8(√3 cos α + sin α)
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