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प्रश्न
In the given figure, AD is the median on BC from A. If AD = 8 cm and BC = 12 cm, find the value of tan x. cot y
उत्तर
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
cos x = `"BD"/"AB" = (6)/(10) = (3)/(5) and sin y = "DC"/"AC" = (6)/(10) = (3)/(5)`
∴ tan x = `"sin x"/"cos x" = (4/5)/(3/5) = (4)/(3) and cot y = "cos y"/"sin y" = (4/5)/(3/5) = (4)/(3)`
∴ tan x. cot y = `(4)/(3) xx (4)/(3) = (16)/(9)`.
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