sir this is the important question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances
it is given that From two points A and B on the same side of a building,
the angles of elevation of the top of the building are 30 and 60 respectively.
If the height of the building is 10 m,
find the distance between A and B correct to two decimal places.
question no 28 , heights and distances , ICSE board
In triangle DBC
tan 600 = 10/BC
Substituting the values
√3 = 10/BC
BC = 10/√3
In triangle DBC
tan 300 = 10/ (BC + AB)
Substituting the values
1/√3 = 10/[10/√3 + AB]
By further calculation
1/√3 [10/√3 + AB] = 10
So we get
AB = 10√3 – 10/√3
Taking LCM
AB = (30 – 10)/ √3
AB = 20/√3
AB = 20√3/3
So we get
AB = (20 × 1.732)/ 3
AB = 20 × 0.577
AB = 11.540 m
Hence, the distance between A and B is 11.54 m.