Question

two boats sail on either sides of a light house.the angle of elevtion from the top of the light house to the first ship is 30 degrees and the angke of depression from the the top of the light house to the second ship is 60 degrees.if the distance between the boats is 120 cm find the height of the lighthouse

Answer 1

Answer:

273.2m

Step-by-step explanation:

Let A and B be the position of two boats (figure)

Let PM be the lighthouse such that PM =100m

Let AM =x and BM =y

In ΔAPM,PMAM=cot30∘

⇒100x=3⇒x=100

Similarly in Δ BPM,

PMBM=cot45∘⇒100y=1⇒y=100m

∴ Required distance, AB=x+y

=1003+100=100(3+1)m=273.2m