Two cargo ships are siling a direct course into harbor. Ship A is 22 miles from harbor. Ship B is sailing into harbor on a course perpendicular to that of ship A. If the angle between them is 47 degrees, how far is ship B from the harbor? Round the answer to the nearest tenth.

Let the harbour be point H.

Is your 47 deg <HAB or <HBA? It makes a difference.

so do you know the answer ?

To find the distance of ship B from the harbor, we can use trigonometry. We have a right triangle formed by ship A, ship B, and the straight line from ship A to the harbor.

Let's label the distance from ship B to the harbor as x.

The angle between ship A and the line to the harbor is 47 degrees. This means that the angle between ship B and the line to the harbor is 90 degrees - 47 degrees = 43 degrees.

Using trigonometry, we can set up the following equation:
tan(43) = x / 22

To solve for x, we can multiply both sides of the equation by 22:
22 * tan(43) = x

Using a calculator, we find that tan(43) ≈ 0.9325. Therefore:
22 * 0.9325 ≈ 20.515

Rounding to the nearest tenth, ship B is approximately 20.5 miles from the harbor.

To find out how far Ship B is from the harbor, we need to use trigonometry.

Let's first visualize the scenario. We have a right triangle where the distance from Ship A to the harbor is the base, the distance from Ship B to the harbor is the height, and the angle between them is 47 degrees.

Now, we know that the trigonometric function for the tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this scenario, the opposite side is the height (distance from Ship B to the harbor), and the adjacent side is the base (distance from Ship A to the harbor).

Using this information, we can set up the equation:

tan(47 degrees) = Opposite / Adjacent

Plugging in the values we have:

tan(47 degrees) = h / 22 miles

Now, we can solve for h (the distance from Ship B to the harbor):

h = tan(47 degrees) * 22 miles

Using a calculator, we find that tan(47 degrees) is approximately 1.0724.

h ≈ 1.0724 * 22 miles ≈ 23.59 miles

Therefore, Ship B is approximately 23.6 miles from the harbor.