From two points A and B on the same side of a building, the angles of elevation of the top of the building are 300 and 600 respectively. If the height of the building is 10 m, find the distance between A and B correct to two decimal places.
From two points A and B on the same side of a building, the angles of elevation of the top of the building are 300 and 600 respectively. If the height of the building is 10 m, find the distance between A and B correct to two decimal places.

Solution:

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.