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 tan x. cot y

Answer 1

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)`.