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Question
In the given figure, AD is the median on BC from A. If AD = 8 cm and BC = 12 cm, find the value of sin x
Solution
Since AD is median on BC, we have
BD = DC = `(1)/(2) xx "BC" = (1)/(2) xx 12` = 6cm
ΔADB is a right-angled triangle.
∴ AB2
= AD2 + BD2
= 82 + 62
= 64 + 36
= 100
⇒ AB = 10cm
ΔADC is a right-angled triangle.
∴ AC2
= AD2 + DC2
= 82 + 62
= 64 + 36
= 100
⇒ AC = 10cm
sin x
= `"AD"/"AB"`
= `(8)/(10)`
= `(4)/(5)`.
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