Question

Two persons on same side of tall building notice the angle of elevation of top of building to be 30 and 60 degree respectively. If the height of building is 72m find distance between two persons.

Answer 1

Answer:

Step-by-step explanation:

See the enclosed picture for the related diagram.

Given Height of the building = AB = 72 m.  The two persons are standing at C and D respectively.

Use trigonometry in the triangles ABC and ABD.

  Tan 60° = AB/BC

  So   BC = 72 / √3   m = 24 √3 meters

  Tan 30° = AB/BD

  So  BD = 72 √3 m

So the distance between the two persons = 48 √3 meters.

Answer 2

Answer:

Step-by-step explanation:

x y

let CD is the building and A & B are the two person. join the point A with D and B with D. from A elevation is 30 degree and from B elevation is 60 degree.

AB = distance between two person = x m

in triangle ACD

tan 30 = CD/AC

1/√3 = 60/AC

AC = 60√3

x+y = 60√3 -----------------(1)

in triangle BCD

tan 60 = CD/BC

√3 = 60/BC

BC = 60/√3

y = 60/√3

put the value of y in equation (1)

x + 60/√3 = 60√3

x = 60√3 - 60/√3

x = 60(3-1)/√3

x = 120/√3

x = 40√3 meter