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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.

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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...
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Given:

  1. 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.

 

 

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