Pythagorean Theorem - How do I know which variable is the hypotenuse?

Question

Reba has found that her new cell phone will operate if it is no more than 17 miles from a cell tower. She lives 8 miles north of the nearest tower. How far west is she able to drive and still have coverage?

Answer 1

I can't include a picture in here, but simply draw a diagram with a tower at point A, her house at point B exactly 8 miles north and then point C somewhere directly west of her house. The segment AB = 8, that is given. We want to locate C such that it is the furthest she can drive...this would be exactly 17 miles from the tower in a straight line. So the hypotenuse, the segment AC would be 17. You've got:

 

8² + BC² = 17²

BC = 289 - 64 = 225

BC = 15

 

Therefore she can drive 15 miles west from her house.

The hypotenuse is just the longest side of a right triangle (i.e. a triangle that contains a right angle)...the side that is NOT on either side of the right angle.

Answer 2

by rule, the hypotenuse is the longest length of the right triangle.

 

based on the question, 17 miles is the hypotenuse. try to sketch a pic of the tower, house, and a car that move west.

 

a² + b² = c²

 

8² + b² = 17²

 

64 + b² = 289

 

b² = 225

 

√(b²) = 15 miles

 

have to go west 15 miles

                  

Answer 3

 Word (story) problems have specific words that translate into concise, precise math variables and operations.  Keep a table of these translations (like you would for Spanish-to-English, for example).

 

The key phrase here is "no more than 17 miles from a cell tower."  Of course, that is a circle with the cell tower at the center.

 

The problem gives the distance from the tower north to Rita's house.  The distance west goes until it intersects the 17-mile circle.  The radius of the circle is the hypotenuse of the triangle.  Beyond that, Rita may not get cell coverage.

 

Oh -- one more note for smart students.  There are "Pythagorean Triples" that appear very, very often in textbooks, homework and standardized tests.  They make the computations easier (since they don't have fractions). This one is 8,15,17.  Another one is 3,4,5.  Another is 5,12, 13.  Think of any more??   (and there may be multiples of these numbers -- like 16,30,34).