Answer:
189.14 miles.
Step-by-step explanation:
This is a vector problem.
A boat sails on a bearing of 73°. This means it is going north, forming a 90° triangle.
The sum of angles in a triangle = 180°
We need to find the third angle.
180° = 90° + 73° + x°
x° = 180° - (90 + 73) °
x = 180° - 163°
x = 17°
The boat then turns and sails 209 miles on a bearing of 190 degrees.
Since it is sailing 190°, it is sailing more than 180°
= 190° - 180° = 10°
This would lead to the formation of another triangle let us call it ABC
Hence, we would have:
90° - ( 10 + 17)°
90° - 27° = 63°
To find the distance of the boat, we would use Cosine rule.
a² = b² + c² - 2bc × Cos A
a = √(b² + c² - 2bc × Cos A
b = 128 miles
c = 209 miles
A = 63°
a = √(128² + 209² -2 × 128 × 209 × Cos 63°)
a = 189.14199miles
Approximately 189.14 miles.
Therefore, the distance of the boat from it's starting point is 189.14 miles.
