Find the distance from Hampton to the point where the beam strikes the shore, as a function of θ. Include a sketch.

Question

Hampton is a small town on a striaght stretch of coastline running north an south. A lighthouse is located 3 miles off shore directly east of hampton. The light house has a revolving searchlight that makes two revolutions per minute. The angle that the beam makes with the east-west line through hampton is called Find the distance from Hampton to the point where the beam striikes the shore, as a function of

Include a sketch

Answer 1

You are creating a right angle along the shore up or down to where the beam meets the shore.

sinC/90 = sinB/θ

θsinC = 90sinB

θ = 90sinB/sinC