Answer:
1) The ship is closer
2) 675.73 m
Step-by-step explanation:
1) The given parameters are;
The initial angle between the ship's course and the lighthouse = 32°
The final angle between the ship's course and the lighthouse = 72°
The distance traveled by the sip between he two positions = 1500 m
Therefore we have a triangle formed between the distance covered by the ship and the two distances of the ship from the lighthouse, a and b
Where;
a = The initial distance fro the lighthouse
b = The final distance fro the lighthouse
The angles of the triangle are
32°, (180 - 72) = 108° and 180 - 32 - 108 = 40°
By sine rule we have;
1500/(sin(40)) = a/(sin(108)) = b/(sin(32)) =
Therefore, a = sin(108°) × 1500/(sin(40°)) = 2219.37 m
b = (sin(32°)) × 1500/(sin(40°)) = 1236.61 m
Therefore, a > b
The initial distance fro the lighthouse > The final distance fro the lighthouse, which shows that the ship is closer
2) By cosine rule we have
a² = b² + c² - 2× b×c×cos(A)
Where the given measurements by Kendra are;
410 m and 805 m with an included (in between) angle of 57°, we have;
Let b = 410 m, c = 805 m, and A = 57°, we have;
a² = 410^2 + 805^2 - 2× 410×805×cos(57 degrees) = 456608.77 m²
a = The length of the stream = 675.73 m.
