Question

A boat sails on a bearing of 73 degrees for 128 miles and then turns and sails 209 miles on a bearing of 190 degrees. Find the distance of the boat from its starting point.

Answer 1

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.