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Difficulty: EasyTriangles and Pythagorean Theorem

A hiker walks 88 miles due north, then turns and walks 1515 miles due east. What is the straight-line distance, in miles, from the hiker's starting point to their current location?

Answer: 17 miles

Answer

17
Because the hiker's path consists of two perpendicular segments (north and east), they form the legs of a right triangle measuring 88 miles and 1515 miles. The straight-line distance from the start to the end is the hypotenuse of this triangle. Applying the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2), we get 82+152=c28^2 + 15^2 = c^2, which simplifies to 64+225=28964 + 225 = 289. The square root of 289289 is 1717. Therefore, the straight-line distance is 1717 miles.

Step-by-Step Solution

1
Visualize the geometrical shape formed by the hiker's path.
A right triangle is formed with legs of 88 miles and 1515 miles.
The directions 'due north' and 'due east' are perpendicular, creating a 90∘90^\circ angle.
2
Set up the Pythagorean theorem equation.
82+152=c28^2 + 15^2 = c^2
The straight-line distance corresponds to the hypotenuse (cc) of the right triangle.
3
Square the values of the legs and add them together.
64+225=28964 + 225 = 289
To evaluate the left side of the equation.
4
Calculate the square root of the sum.
c=289=17c = \sqrt{289} = 17
To solve for cc and find the final straight-line distance.

Key Concept

Calculating distance using the Pythagorean theorem
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Topics

Triangles and Pythagorean Theorem

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