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 60

^{0}= 10/BCSubstituting the values

√3 = 10/BC

BC = 10/√3

In triangle DBC

tan 30

^{0}= 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.