Given triangle ABC, and D is a midpoint of side BC, find the numerical value of AD^2, if AB = 4, BC = 8 and AC = 6.?
回答 (1)
2017-10-31 5:49 pm
AD² = AB × AC - BD × DC
AD² = 4 × 6 - (8/2) × (8/2)
AD² = 8
AD = √8
AD = 2√2
In ΔABC :
AC/sin∠ABC = BC/sin∠BAC (sine law)
sin∠BAC/sin∠ABD = BC/AC
sin∠BAC/sin∠ABD = (8 cm)/(6 cm)
Hence, sin∠BAC/sin∠ABD = 4/3
AD² = 4 × 6 - (8/2) × (8/2)
AD² = 8
AD = √8
AD = 2√2
In ΔABC :
AC/sin∠ABC = BC/sin∠BAC (sine law)
sin∠BAC/sin∠ABD = BC/AC
sin∠BAC/sin∠ABD = (8 cm)/(6 cm)
Hence, sin∠BAC/sin∠ABD = 4/3
收錄日期: 2021-04-18 17:58:59
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