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Dima020 [189]
1 year ago
9

two ships leave a port at the same time. the first ship sails on a bearing of 55° at 12 knots (natural miles per hour) and the s

econd on a bearing of 145° at 22 knots. how far apart are they after 1.5 hours
Mathematics
1 answer:
Korvikt [17]1 year ago
8 0

Answer:

37.59 nautical miles

Explanation:

Distance = Speed x Time

The speed of the first ship = 12 knots

Thus, the distance covered after 1.5 hours

\begin{gathered} =12\times1.5 \\ =18\text{ miles} \end{gathered}

The speed of the second ship = 22 knots

Thus, the distance covered after 1.5 hours

\begin{gathered} =22\times1.5 \\ =33\text{ miles} \end{gathered}

The diagram representing the ship's path is drawn and attached below:

The angle at port = 90 degrees.

The triangle is a right triangle.

Using Pythagorean Theorem:

\begin{gathered} c^2=a^2+b^2 \\ c^2=18^2+33^2 \\ c^2=324+1089 \\ c^2=1413 \\ c=\sqrt[]{1413} \\ c=37.59\text{ miles} \end{gathered}

The two ships are 37.59 nautical miles apart after 1.5 hours.

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Step-by-step explanation:

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*Note the ">" sign is similar to the "=" sign.

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3 years ago
To the nearest tenth, what is the perimeter of the triangle with vertices at (−2, 3), (3, 6), and (2, −2)?
katovenus [111]

9514 1404 393

Answer:

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Step-by-step explanation:

The distance formula can be used to find the side lengths.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

For the first two points, ...

  d = √((3 -(-2))^2 +(6 -3)^2) = √(5^2 +3^2) = √34 ≈ 5.83

For the next two points, ...

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For the last and first points, ...

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Then the sum of the side lengths is ...

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The perimeter of the triangle is about 20.3 units.

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3 years ago
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pantera1 [17]
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6 0
3 years ago
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