A naval patrol vessel leaves port and sails due South for 10\text{ nautical miles}. It the… — Armed Services Vocational Aptitude Battery (ASVAB)

A naval patrol vessel leaves port and sails due South for $10\text{ nautical miles}$ . It then changes course and sails due West. After completing this leg of the journey, the vessel's radar indicates it is exactly $26\text{ nautical miles}$ in a straight line from the port. How many nautical miles did the vessel travel due West?

A
$16$
$24$ Answer
C
$36$
D
$576$

Answer

The vessel traveled

24

nautical miles due West.

The path of the vessel forms a right triangle. The straight-line distance from the port is the hypotenuse (

26\text{ nautical miles}

), and the southward distance is one leg (

10\text{ nautical miles}

). Using the Pythagorean theorem (

a^2 + b^2 = c^2

), we substitute the known values:

10^2 + b^2 = 26^2

. This simplifies to

100 + b^2 = 676

. Subtracting

100

from both sides gives

b^2 = 576

. Taking the square root of

576

yields

24\text{ nautical miles}

Step-by-Step Solution

Identify that the vessel's path forms a right triangle.

The southward path (

10

) and westward path (

x

) are the legs, and the straight-line distance (

26

) is the hypotenuse.

South and West directions are perpendicular, creating a 90-degree angle.

Set up the Pythagorean theorem equation (

a^2 + b^2 = c^2

10^2 + x^2 = 26^2

This formula relates the lengths of the legs to the hypotenuse in a right triangle.

Square the known values.

100 + x^2 = 676

To begin isolating the unknown variable

x

Subtract

100

from both sides of the equation.

x^2 = 576

To completely isolate the

x^2

term.

Take the square root of both sides.

x = 24

To find the final distance traveled due West.

Key Concept

Applying the Pythagorean theorem to find the missing leg of a right triangle.

Estimated Time:1m 0s

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