The bearing of a lighthouse from a ship was found to be n 37 degrees e. after the ship sailed 2.5 miles due south, the new bearing was n 25 degrees east. find the distance between the ship and the lighthouse at each location.

The distance between the lighthouse and the ship

from the start position A = 5.08 miles

from the Final point B = 7.23 miles

Explanation:

Note: Refer the figure

Let the position of the lighthouse be 'L'  

Given:

When the ship is at the position A, ∠DAL=37°

Now, when the ship sails through a distance of 2.5 i.e at position B

mathematically,

AB=2.5 miles

∠ABL=25°

Now,

∠DAL + ∠LAB = 180°

or

37° +  ∠LAB = 180°

or

∠LAB = 180° - 37° = 143°

Also, In ΔLAB

∠LAB + ∠ABL + ∠ALB = 180°

or

143° + 25° + ∠ALB = 180°

or

∠ALB = 180° - 143° - 25° = 12°

Now using the concept of the sin law

In ΔLAB

or

AL = 5.08 miles

and,

or

BL = 7.23 miles

hence,

The distance between the lighthouse and the ship

from the start position A = 5.08 miles

from the Final point B = 7.23 miles

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards