From the top of a lighthouse 75 m high,the angles of depression of two ships are observed to be 30and 45 respectively if one ship directly behind the other on the same side of the lighthouse then find the distance betwwen the two ships
Answers
Answered by
1
Let AB is the light house. So AB = 75
From triangle ABC,
tan 45 = AB/BC
=> 1 = 75/BC
=> BC = 75
Again from triangle ADC
tan30 = AB/BD
=> 1/√3 = AB/(BC + CD)
=> 1/√3 = 75/(75 + CD)
=> 1/√3 = 75/(75 + CD)
=> 75 + CD = 75√3
=> CD = 75√3 - 75
=> CD = 75(√3 - 1
From triangle ABC,
tan 45 = AB/BC
=> 1 = 75/BC
=> BC = 75
Again from triangle ADC
tan30 = AB/BD
=> 1/√3 = AB/(BC + CD)
=> 1/√3 = 75/(75 + CD)
=> 1/√3 = 75/(75 + CD)
=> 75 + CD = 75√3
=> CD = 75√3 - 75
=> CD = 75(√3 - 1
Similar questions