Answer:
a ≈ 117 cm
Step-by-step explanation:
Using sine rule on triangle ABC as re - shown in the attachment below to get side AC first we have;
∠A = 34°, BC = 164cm, ∠B = 27°, AC = ?
AC/sin 27° = BC/sin 34°
AC/sin 27° = 164/sin 34°
AC = 164 * sin 27° / sin 34°
AC = 74.45/0.5592
AC = 133.14 cm
To get the side 'a', we will use the trig ratio SOH CAH TOA on the right angled ACD.
According to SOH,
sin 61° = a/AC
a = ACsin61°
a = 133.14 * sin 61°
a = 116.45
a ≈ 117 cm
The marked side is approximately 117 cm
