Question

from the adjoining figure find AC

Answer 1

Step-by-step explanation:

In triangle ABC

tan 30°=AC/BC

1/root3 =AC/40+DC

40+DC=root 3 AC_(i)

In triangle ADC

tan45°=AC/DC

1=AC/DC

AC=DC_(ii)

put value of DC IN (i)

40+AC=root3 AC

40=Root 3 AC-AC

40=AC(root3-1)

40/(root3-1)=AC

on rationalizing

AC=20(root 3+1)

or

AC=20(1.732+1)

AC=20×2.732

AC=54.64