Question

25. A large ship is sailing between three small islands. To do so, the ship must sail between two pairs of islands, avoiding sailing between a third pair. The safest route is to avoid the closest pair of islands. Which is the safest route for the ship?

26. Three cell phone towers form APQR.
The measure of ZQ is 10° less than the measure of LP. The measure of Ris 5° greater than the measure of ZO. Which two towers are closest together?

Answer 1

The questions involve mathematical concepts in geometry and vector operations, used to navigate a ship among islands, identify the closest cell phone towers, and determine the location of a boat after traveling in specified directions.

Step-by-step explanation:

The student is asking questions that involve the subject of mathematics, specifically geometry and vector operations. In the context of the given scenarios which involve sailing and flying, these problems are looking at determining the safest route, calculating distances through vector analysis, and using trigonometry and the Pythagorean theorem.

To determine the safest route for a ship among islands, we would need more information about the distances between each pair of islands. Assuming that the ship avoids the closest pair, we calculate the distances using trigonometry. With the phone towers forming APQR, we apply geometry principles to infer which towers are closest based on the given angle measures.

When working with vector subtraction graphically, as in the example of a woman sailing a boat, we use the vector displacement concept combined with trigonometry to determine her final position relative to the dock. This demonstrates how the direction and magnitude of vectors influence the outcome of navigational tasks.

Answer 2

These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.

Step-by-step explanation:

We must first locate the three pairs of islands in order to establish which pair is nearest before determining the safest route for the ship.

Give the three islands the letters A, B, and C. The three island groups are designated as AB, AC, and BC. Finding the closest pair is necessary.

We can leverage the separation between the islands to do this. Assuming that the islands are separated by the following distances:

A and B are separated by 10 nautical miles.

A and C are separated by 15 nautical miles.

B and C are separated by 12 nautical miles.

These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.