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:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 96
Let AB = x meter ( height of building)
Now, In AMB
tanθ = AB/AM
tanθ = X/72
Again, In ANB
tan(90-θ) = AB/AN ( ANB and AMB are complementary angles)
cotθ = x/128
tanθ = 128/x
So, x/72 = 128/x
x2 =128 ×72
x2 = 64×144
x =8×12 = 96