the angles of depression of the top and bottom of a 8m tall building from the top of a multi storeyed building are 30 and 60 respectively.find the height of multi storeyed building an distance between the two buildings.

Consider triangles ABE & ACD. Considering given angles of depression, 30 & 60 degrees as angles of elevation of angleE & D respectively. ED is the height of the building which is 8m. Now,

EB=DC(distance b/w buildings) & ED=BC.

In triangle ABE,

Tan30=AB/EB ---- EB=ABroot3=DC

In Triangle ACD,

Tan60= AB+BC/DC ----- root3 = AB+8/ABroot3

3AB=AB+8 ------2AB=8

AB=4m

Hence, height of multi-storey building= AB+BC=4+8= 12m