Question

A ship is traveling around the outside rim of an island surveying a good place to land. If it is 10 miles from a lighthouse at the center of the island and 45° from due north, how far has the ship traveled from the most northern tip of the island to the nearest tenth?
0.8 miles
4.5 miles
7.9 miles
12.5 miles

Answer 1

@nincompoop

Answer 2

Wait a second.

Answer 3

yes?

Answer 4

pi R = 8
then R = 4 ÷ π= 1.2732395447351628 cm

Answer 5

wouldn't the radius be 10 since the ship is at the edge and the lighthouse is in the middle?

Answer 6

Convert it into mile.

Answer 7

The entire circumference of the circle makes 360 degrees at the center.
Arc length Ab makes 45 degrees at the center.
They are proportional.
Arc length AB / 45 degrees = Circumference of circle / 360 degrees.
Arc length AB = 2 * pi *r * 45 / 360

Answer 8

put r = 10 above and calculate AB.

Answer 9

This is a direct proportions problem.
360 degrees represent circumference of the circle.
45 degrees will represent how much of the circle?
45/360 * circumference of circle =
1/8 * circumference of circle = 1/8 * 2 * pi * 10 = ?

Answer 10

7.85?

Answer 11

so the answer would be 7.9?

Answer 12

Yes, 7.9 miles.

Answer 13

Yaya this was correct! (Just took the quiz) tyy