A surveillance camera is mounted on the top of an 80 m tall building. The angle of elevation from the camera to the top of another building is 42 degree. The angle of depression from the camera to...

A surveillance camera is mounted on the top of an 80 m tall building. The angle of elevation from the camera to the top of another building is 42 degree. The angle of depression from the camera to the bottom of the same building is 32 degree. How tall is the other building?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A surveillance camera is mounted on the top of an 80 m tall building. The angle of elevation from the camera to the top of another building is 42 degree. The angle of depression from the camera to the bottom of the same building is 32 degree.

Let the height of the other building be H. It is possible to divide the height of the building into two parts. One part that is above the camera on the 80 m tall building and has a length H - 80 and the other that lies below the camera and has a height of 80 m.

If the distance of the building with the camera from the other building is D, we have

tan 42 = (H - 80)/D and tan 32 = 80/D

tan 32 = 80/D

=> D = 80/tan 32

substituting in tan 42 = (H - 80)/D

=> tan 42 = (H - 80)/(80/tan 32)

=> tan 42*80 = tan 32*(H - 80)

=> H - 80 = 80*tan 42/tan 32

=> H = 80 + 80*tan 42/tan 32

=> H = 195.27 m

The height of the other tower is 195.27 m

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