(Q8)In △ABC, right angle is at B, AB = 5 cm and ∠ACB = 30°. Determine the lengths of the sides BC and AC.

ABC5cm30°

Given AB=5 cm and ∠ACB=30°. To find the length of side BC,we will choose the trignometric ratio involving BC and the given side AB. Since BC is the side adjacent to angle C and AB is the side opposite to angle C.

Therefore,

BC
 = tan C
i.e.
BC
 = tan 30° =
1
√

which gives BC = √3 cm

Now, by using the trignometric ratios in △ABC

sin 30° =
AC
1
 =
AC

AC = cm