The two line between the two lighthouses, and the lines from
each lighthouse to the ship form a triangle.
Correct response:
- The shortest distance from a lighthouse to the ship is approximately 30.64 km
Which method can be used to find distance from the ship
Distance between the two lighthouses = 20 km
Angle formed by the line between the two lighthouses and
the ship from lighthouse A = 50°.
The similar angle formed from lighthouse B = 100°
Required;
The shortest distance from a lighthouse to a ship.
Solution:
The angle formed by the lines to the two lighthouses from the ship, θ, is given as follows;
θ = 180° - 100° - 50° = 30°
Angle θ = The angle opposite to the line AB between the two lighthouses
By law of sines, we have;
[tex]\mathbf{\dfrac{20 \ km}{sin(30^{\circ})}} = \dfrac{x}{sin(50^{\circ})} = \dfrac{y}{sin(100^{\circ})}[/tex]
Where;
x = The distance from the ship to lighthouse B
y = The distance from the ship to lighthouse A
Which gives;
[tex]x = sin(50^{\circ}) \times \dfrac{20 \ km}{sin(30^{\circ})} \approx \mathbf{30.64 \ km}[/tex]
[tex]y = sin(100^{\circ}) \times \dfrac{20 \ km}{sin(30^{\circ})} \approx \mathbf{ 39.39 \ km}[/tex]
- The shortest distance from a lighthouse to the ship is x ≈ 30.64 km
Learn more about the law of sines here:
https://brainly.com/question/8242520
