Question

A boat travels 8 miles north from point A to point B. Then it moves in the direction S 40º W and reaches point C. Finally, it turns S 40º E and returns to point A. The total distance covered by the boat is miles.

Answer 1

The total distance covered by the boat is 18.44 miles.

Answer 2

The distance covered by boat is 18.44 miles.

Explanation:

Use the given information to draw a figure.

`\angle B=\angle BCN=40^(\circ)` (Alternate interior angles)

`\angle BCN+\angle BCA+\angle ACS=180^(\circ)` (Supplementary angles)

`40^(\circ)+\angle BCA+40^(\circ)=180^(\circ)`

`\angle BCA=100^(\circ)`

According to angle sum property of a triangle, the sum of interior angles is 180 degree.

`\angle A+\angle B+\angle BCA=180^(\circ)`

`40^(\circ)+\angle B+100^(\circ)=180^(\circ)`

`\angle B=40^(\circ)`

Since two angles are same, therefore ABC is isosceles triangle.

`BC=AC`

Use Law of Sine:

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

`(BC)/(\sin A)=(AC)/(\sin C)`

`(BC)/(\sin 40)=(8)/(\sin 100)`

`BC=(8)/(\sin 100)* \sin 40=5.22`

`BC=AC=5.22`

The perimeter of triangle ABC is

`AB+BC+CA=8+5.22+5.22=18.44`

Therefore the distance covered by boat is 18.44 miles.