Question

The angles of depression of two cars on a straight road as observed from the top of a 42m high building are 60° and 75° respectively. Find the distance between the cars if they are on opposite sides of the building. 

Answer 1

Let the position of the two cars be A and C. Let BO be the building of height 42 m. 

In ΔBAD,

`tan75^circ = "BD"/"AD"`

⇒ `3.7321 = 42/"AD"`

⇒ `"AD" = 42/3.7321`   

⇒ AD = 11.25              ....(1)

In ΔBDC,

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

⇒ `sqrt(3) = 42/"DC"`

⇒ `"DC" = 42/1.732 = 24.25`   ....(2)

∴ AC = AD+ DC = 11.25 m + 24.25 m = 35.5 m 

Thus, the distance between the cars is 67.63 m.