Triangle ABC =10cm angle abc=30 and angleBAC= 45. A perpendicular from C to meet ABatD

Answer 1

To find the length of CD, we can use trigonometry.

First, we need to find the lengths of AC and BC using the sine rule:

AC/sin 30 = 10/sin 45
AC = 10 * sin 30 / sin 45
AC ≈ 5.77 cm

BC = 10 - AC
BC ≈ 4.23 cm

Now, we can use the sine rule in triangle ACD to find the length of CD:

CD/sin 45 = BC/sin 30
CD = BC * sin 45 / sin 30
CD ≈ 3.09 cm

Therefore, the length of CD is approximately 3.09 cm.