(a) To find out how far the ship must now sail to reach its original destination, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the ship's northward and eastward journeys form the two sides of a right triangle, and the direct path to the original destination is the hypotenuse.

So, we calculate the length of the hypotenuse as follows:

√((120 km)^2 + (100 km)^2) = √(14400 km^2 + 10000 km^2) = √24400 km^2 = 156.2 km

So, the ship must now sail approximately 156.2 km to reach its original destination.

(b) To find out in what direction the ship must now sail, we can use trigonometry. Specifically, we can find the angle θ between the north direction and the path to the original destination using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

So, we calculate θ as follows:

tan(θ) = (100 km) / (120 km) = θ = arctan((100 km) / (120 km)) = 39.8 degrees

Since the angle is measured from the north direction, the ship must now sail approximately 39.8 degrees east of north to reach its original destination.

Question

(a) To find out how far the ship must now sail to reach its original destination, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the ship's northward and eastward journeys form the two sides of a right triangle, and the direct path to the original destination is the hypotenuse.

So, we calculate the length of the hypotenuse as follows:

√((120 km)^2 + (100 km)^2) = √(14400 km^2 + 10000 km^2) = √24400 km^2 = 156.2 km

So, the ship must now sail approximately 156.2 km to reach its original destination.

(b) To find out in what direction the ship must now sail, we can use trigonometry. Specifically, we can find the angle θ between the north direction and the path to the original destination using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

So, we calculate θ as follows:

tan(θ) = (100 km) / (120 km) => θ = arctan((100 km) / (120 km)) = 39.8 degrees

Since the angle is measured from the north direction, the ship must now sail approximately 39.8 degrees east of north to reach its original destination.

Knowee AI · Accepted Answer

(a) To find out how far the ship must now sail to reach its original destination, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the ship's northward and eastward journeys form the two sides of a right triangle, and the direct path to the original destination is the hypotenuse.

So, we calculate the length of the hypotenuse as follows:

√((120 km)^2 + (100 km)^2) = √(14400 km^2 + 10000 km^2) = √24400 km^2 = 156.2 km

So, the ship must now sail approximately 156.2 km to reach its original destination.

(b) To find out in what direction the ship must now sail, we can use trigonometry. Specifically, we can find the angle θ between the north direction and the path to the original destination using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

So, we calculate θ as follows:

tan(θ) = (100 km) / (120 km) => θ = arctan((100 km) / (120 km)) = 39.8 degrees

Since the angle is measured from the north direction, the ship must now sail approximately 39.8 degrees east of north to reach its original destination.

A ship sets out to sail to a point 120 km due north. An unexpected storm blows the ship to a point 100 km due east of its starting point. (a) How far and (b) inwhat direction must it now sail toreach its original destination?

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