Answer:
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
[tex]\frac{AL}{sin25^o}=\frac{2.5}{sin12^o}[/tex]
or
AL = 5.08 miles
and,
[tex]\frac{BL}{sin143^o}=\frac{2.5}{sin12^o}[/tex]
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
The distance between the lighthouse and the initial ship position is 5.08 miles
The distance between the lighthouse and the new ship position is
7.24 miles
Bearing is angular measurement in degrees used to trace a location or position while distance refers to extent covered during the movements
The problem gives a triangle NSL
N = New ship position, side opposite this angle = n
S = Initial location of the ship, side opposite this angle = s
LL = Lighthouse location, side opposite this angle = L
<S = 180 - 37 = 143
<N = 25 (given)
<LL = 180 - (143 + 25) (sum of angles of a trianlge)\
<LL = 12
L = 2.5 miles (given)
using sine rule
sine N / n = sine S / s = sine LL / L
first distance to be foumd = n
n = distance between the lighthouse and the initial ship position
sine N / n = sine LL / L
sine 25 / n = sine 12 / 2.5
n = ( sine 25 * 2.5 ) / sine 12
n = 5.08 miles
second distance to be foumd = s
s = distance between the lighthouse and the new ship position
sine S / s = sine LL / L
sine 143 / s = sine 12 / 2.5
s = ( sine 143 * 2.5 ) / sine 12
s = 7.24 miles
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