Question

The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45° and 30° respectively.If the ships are 200m apart ,find the height of the lighthouse

Answer 1

Let top point of the light house A, a point B on the horizontal line through A in the plane of light house and the two ships .Height of the light house h and its foot rest point is C , point focused of the nearer ship is D and 200 m apart is E .

angle BAE=AEC=30° ,

angle BAD=ADC=45°

AC/CE=Tan 30°=1/√3, CE/AC=√3

AC/CD= Tan 45°= 1 , CD/AC=1

(CE/AC) - (CD/AC) =√3–1

(CE-CD)/AC=0.732

200/AC=0.732

AC=200/0.732= 273.22 m

Height of the lighthouse =273.22 m

Answer 2

Let top point of the light house A, a point B on the horizontal line through A in the plane of light house and the two ships .Height of the light house h and its foot rest point is C , point focused of the nearer ship is D and 200 m apart is E .

angle BAE=AEC=30° ,

angle BAD=ADC=45°

AC/CE=Tan 30°=1/√3, CE/AC=√3

AC/CD= Tan 45°= 1 , CD/AC=1

(CE/AC) - (CD/AC) =√3–1

(CE-CD)/AC=0.732

200/AC=0.732

AC=200/0.732= 273.22 m

Height of the lighthouse =273.22 m