Respuesta :
The initial 50 miles distance from the lighthouse and the N 30° W and N 40° W bearing of the ship before and after traveling due east, using the law of sines, indicates.
- After travelling due east the ship is approximately 56.53 miles from the lighthouse.
What is the law of sines?
The law of sines states that in a triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for each of the three sides of the triangle.
The distance of the ship from the lighthouse = 50 miles
Bearing of the lighthouse from the ship = N 30° W
The direction in which the ship travels = due east
The new bearing to the lighthouse = N 40° W
In the triangle formed by the initial and new locations of the ship and the lighthouse, the interior angles, A, B, C are;
m∠A = 30° + 90° = 120°
m∠B = 90° - 40° = 50°
Therefore; m∠C = 180° - (120° + 50°) = 10°
Angle opposite the initial distance of the ship from the lighthouse = ∠B = 50°
The angle opposite the new distance of the ship from the lighthouse = m∠A = 120°
The law of sines indicate that we have;
[tex]\dfrac{50}{sin(50^{\circ})} = \dfrac{New \, distance}{sin(120^{\circ})}[/tex]
50 × sin(120°) = The new distance of the lighthouse × sin(50°)
The new distance of the lighthouse = 50 × sin(120°)/(sin(50°)) ≈ 56.53
- The distance of the ship from the lighthouse after travelling due east is approximately 56.53 miles
Learn more about the law of sines here:
https://brainly.com/question/19149891
#SPJ1
