A boat tavels 8mi N from A to B then moves S 40 degrees W to C turns S 40 degrees E to A, total distnace?

Question

a. 14.95 miles

b. 18.44 miles

c. 20.04 miles

d. 25.88 miles

Answer 1

Hi Jacey, if a boat travels north for 8 miles from A to B, then turns south of west 40, last turns south of east 40 degrees, the boat travels in a triangle, actually an isosceles triangle. The two sides from B to C and from C to A are the same lengths.

 

If we drop a line from point C straight to line AB making a right angle on line AB, it will cut the line AB in two equal parts of 4 miles each.

 

 

In a right triangle if we know one of the angles, we can find the other one. We have one angle of 40 degrees, then 90 - 40 equals 50, or the other angle in the right triangle.

 

We can use angle 50 plus the length of 4 miles to find the hypotenuse or the distance from point B to C of the right triangle.

 

The relationship is: side a / hypotenuse = sin 50.

 

Side a = 4 miles, one half of the distance from A to B.

 

Solve for the hypotenuse:

 

4 / hypotenuse = sin 50

 

4 / sin 50 = hypotenuse

 

hypotenuse or the distance from point B to C = 5.22 miles.

 

Since the distance from point B To C is equal to the distance from point C to A, the distance from point C to A is also 5.22 miles.

 

Total distance traveled is: 8 + 5.22 + 5.22 or 18.44 miles.

 

Questions?