9. The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings.

Given: The angles of depression from the top and bottom of the 8 m tall building are 30° and 45°, respectively. We can form two right triangles to represent the situation. For the top of the 8 m tall building: tan⁡(30∘)=8dtan(30∘)=d8 For the bottom of the 8 m tall building: tan⁡(45∘)=8dtan(45∘)=d8 We can solve these two equations simultaneously to find the values of hh and dd. First, let's solve for dd using either equation (they are the same): tan⁡(30∘)=8dtan(30∘)=d8 13=8d3 1=d8 d=83d=83 Now, using the value of dd, we can find the height of the multi-storeyed building using either equation: tan⁡(30∘)=hdtan(30∘)=dh 13=h833 1=83 h h=8h=8 So, the height of the multi-storeyed building is 8 meters, and the distance between the two buildings is 8383 meters. read less