Unformatted text preview: K = 1 2 AC Â· BD sin Î¸ . 9. From formula (2.26) derive the following formula for the area of a triangle â–³ ABC : Area = K = a 2 sin B sin C 2 sin ( B + C ) 10. Show that the triangle area formula Area = K = 1 4 R ( a + ( b + c ))( c âˆ’ ( a âˆ’ b ))( c + ( a âˆ’ b ))( a + ( b âˆ’ c )) is equivalent to Heronâ€™s formula. ( Hint: In Heronâ€™s formula replace s by 1 2 ( a + b + c ) . ) 11. Show that the triangle area formula (2.34) is equivalent to Heronâ€™s formula. ( Hint: Factor the expression inside the square root. ) 12. Find the angle A in Example 2.16, then use formula (2.23) to Â±nd the area. Did it work? 11 Due to the Chinese mathematician Qiu Jiushao (ca. 12021261)....
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 Fall '11
 Dr.Cheun
 Calculus, Angles, triangle, Heron's formula, Triangle Area Formula, Heronâ€™s formula

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