The angle of elevation of the top of a tall building from the points M and N at the distances of 72 ...........

Quantitative Aptitude (CGL) Height and Distance

The angle of elevation of the top of a tall building from the points M and N at the distances of 72 m and 128 m, respectively,

from the base of the building and in the same straight line with it, are complementary. The height of the building (in m) is:

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SSC CGL 12th April 2022 Shift-2

To find the height of the building, consider these points:

- The angles of elevation from M and N are complementary, meaning they add up to 90 degrees.

- If we let the angle of elevation from M be ?, then the angle of elevation from N is 90° - ?.

- From point M, the height of the building can be calculated using tan(?) = height / 72.

- From point N, the height of the building can be calculated using tan(90° - ?) = height / 128, which simplifies to cot(?) = height / 128.

- Since tan(?) = 1/cot(?), combining the two equations gives height/72 = 128/height.

Solving height² = 9216 gives the height = 96 m.

- Therefore, the building's height is 96 m.

Option 2: 96

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