A light house ,facing north, sends out fan shaped beam of light extending from NE (north east) to NW (northwest) - Maths - Some Applications of Trigonometry

Question

A light house ,facing north, sends out fan shaped beam of light
extending from NE (north east) to NW (northwest) An observer on a
steamer sailing due west ,first sees the light when he is 5 km away
from the lighthouse and continues to see it for 30√2 minutes
Then , find the speed of the steamer

Tanveer Sofi · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_55b3c3f6a8bd8%20png"
style=
"width: 250px; height: 235px;">If the situation in the question is represented diagramatically for the light house at A,the sides AB and AC  of the  triangle ABC  represent the NW and NE directions respectively
As NW and NE directions are perpendicular to each other,therefore angle A of triangle ABC is right angle
The side CB represents, the path of the steamer, as it is sailing due west
Also, as the steamer sails only in the west direction, the  sides of the triangleAC and AB are equal
Now, the observer on the steamer first sees the light when the steamer reaches point B
Therefore according to the question;AB=5 kmand AC=5 kmIn right angled triangle ABC, by pythagoreous theorem:CB2=AB2+AC2=2 AB2                    As, AB=AC⇒CB2=2×52⇒CB=52 kmThe time taken by the steamer to cross the length CB is 302 minutes
Therefore, the speed of the steamer=length of CBtime taken=52302 km/ minute =16 km/ minute

A light house ,facing north, sends out fan shaped beam of light extending from NE (north east) to NW (northwest).An observer on a steamer sailing due west ,first sees the light when he is 5 km away from the lighthouse and continues to see it for 30√2 minutes .Then , find the speed of the steamer.