Question

A captain of a boat has used a weather radar system to detect a storm. The

captain was originally making a straight line to shore, about 100 miles away.
Instead, the captain must turn 34 degrees port side (left), then turn 126 degrees
starboard (right). How much farther does the boat have to travel due to the
detour?

Answer 1

The boat has to travel approximately 94.86 miles farther due to the detour.

Step-by-step explanation:

To find out how much farther the boat has to travel due to the detour, we need to calculate the distance covered in the original straight line and compare it with the distance covered after the turns.

The original distance to shore is 100 miles.

After turning 34 degrees port side, the boat changes direction and covers a new distance. We can use the Law of Cosines to calculate this distance:

d1 = sqrt(100^2 + 100^2 - 2 * 100 * 100 * cos(34))

d1 ≈ 132.91 miles.

Then, after turning 126 degrees starboard, the boat changes direction again and covers another new distance. We can use the Law of Cosines once again to calculate this distance:

d2 = sqrt(132.91^2 + 100^2 - 2 * 132.91 * 100 * cos(126))

d2 ≈ 194.86 miles.

Therefore, the boat has to travel approximately 194.86 - 100 = 94.86 miles farther due to the detour.