Question

find the length of cd

Answer 1

Hi !

Let BC be "b" .

 In Δ DCA ,
tan x° = CD/AC

CD/AC = 5/12

CD/AB+BC = 5/12

CD/48 + b = 5/12

5(48 + b) = 12 CD

CD = 5(48 +b)/12      -----> (1)

 In Δ DCB ,

tan y° = CD /BC

CD/BC = 3/4

CD/b = 3/4

3b = 4 CD

CD = 3 b / 4             -----> (2)

Equation (1)  = equation (2)


5(48 +b)/12   = 3b/4

Cross multiply ,

36 b = 4*{5(48 + b)}

36 b = 4{ 240 + 5b }

36b = 960 + 20 b

16 b = 960

b = 960/16

b = 60

From eqn(2),

CD = 3b/4
      = 3*60/4
      = 180/4
      = 45 m

Length of CD is 45 m