Question

Two persons standing on opposite sides of a tower observe the angles of elevation of the top of the tower to be 60° and 50° respectively. Find the distance between them, if the height of the tower is 80m. 

Answer 1

Let the position of the two persons be A and C. Let BD be the tower of height 80 m. 

In ΔBAD,

`tan60^circ = "BD"/"AD"`

⇒ `sqrt(3) = 80/"AD"`

⇒ `"AD" = 80/sqrt(3)`

⇒ AD = `(80sqrt(3))/3 = (80 xx 1.732)/3` = 46.19 ...(1)

In ΔBDC,

`tan50^circ = "BD"/"DC"`

⇒ `1.1918 = 80/"DC"`

⇒ `"DC" = 80/1.1918 = 67.13`  ....(2)

:. AC = AD + DC = 46.19 m + 67 .13 m = 113.32 m 

Thus, the horizontal distance between the two persons is 113. 32 m.