Finding the Length of the Hypotenuse

The formula can be changed around to find the length of an unknown side when the other two sides are known.

The formula is used to find
the length of the hypotenuse when the
lengths of the two legs are known.

In this example, we know the length of the legs
a and b, but not the length of the hypotenuse, c.

To find the length of the hypotenuse,

• Replace the variables of the formula with the lengths of the legs.
• Do the calculations. The answer is the length of the hypotenuse c.

Here is this formula worked on the calculator.

Remember: the keys and react to whatever is on the display when they are pushed.

10' is the length of the hypotenuse.

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Hypotenuse length practice: Find the length of the hypotenuse using the two sides given. Convert the numbers with units of measurement to include fractions. Round off the rest of the numbers to 4 decimal places. Remember:

If you have difficulty squaring mixed numbers, refresh your memory here.

           a           b                 a           b

     (1)   6           9           (7)  9'4 3/4"    12'11" 
     (2)   5          10           (8)   1.73"       2.32" 
     (3)  22"         33"          (9) 104'3"       77'7"  
     (4)   2.5"        7.5"       (10)  19          25 
     (5)  10 3/8"     7 7/16"     (11)  16 15/16"   22 15/16"  
     (6)  7'8"        3'6"        (12)  24          24 

Answers.