Lighthouse a and lighthouse b are located on opposite sides of the mouth of the bay harbor at vertices a and b, respectively. if a ship heading into the harbor is locate at vertex s what is m angle s

Step-by-step explanation:

How Fast is the Lighthouse Beam Moving?

Date: 10/13/2002 at 20:29:57

From: Leigh

Subject: Rates and derivatives

A lighthouse is located on a small island 3 km away from the nearest

point P on a straight shoreline, and its light makes four revolutions

per minute. How fast is the beam of light moving along the shoreline

when it is 1 km away from P?

Date: 10/15/2002 at 13:45:29

From: Doctor Roy

Subject: Re: Rates and derivatives

Hi,

Thanks for writing to Dr. Math.

Let's draw a quick picture to make the situation clearer:

            3km

    L P

       \             |

         \           |

           \         |

             \       | 1km

         x     \     |

                 \   |

                   \ |

                     A

Please note that the picture is not to scale. Point A is where

the beam of light hits the shore when it is 1 km away from P, and

x represents the length of the beam of light from the lighthouse.

We can find the value of x by using the Pythagorean theorem:

      x^2 = 1^2 + 3^2

      x^2 = 1 + 9

      x^2 = 10

        x = sqrt(10)

So, x is sqrt(10) km long, or roughly 3.16 km long.

Another fact we need to know is the rotational speed of the

lighthouse. The lighthouse beam makes 4 full revolutions in a minute.

So, we can express this as:

    w = 4 rev/min

Do you remember the formula for the circumference of a circle? It is

given by:

    C = 2*pi*r