Question

if tan xº =5/12
tan yº 3/4 and
AB = 48 m; find
the length of CD​

Answer 1

Answer:

CD = 45

Step-by-step explanation:

tan x = Perp/Base = DC/AC

tan y = Perp/Base = DC/BC

tanx/tan y =(DC/AC)/ (DC/BC ) = (DC/AC) *(BC/DC)= BC/AC

By substituting given values for tanx and tan y we get

tan x/tan y=(5/12)/(3/4) = (5/12)*(4/3) = 5/9

BC/AC = 5/9 I.e. 9BC = 5AC

Since AC=AB+BC, 5AC = 5(AB+BC) = 5AB+5BC

9BC = 5AB+5BC I.e. 4BC= 5AB = 5*48 = 240 BC = 60m

tan y = Perp/Base = DC/BC = DC/60

But it is given that tan y = 3/4

Hence 3/4 = DC/60 DC = (3/4)*60 = 45M