Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 9-4

Example 1	Find the Length of the Hypotenuse
Find the length of the hypotenuse of the right triangle.

     c^2 = a^2 + b^2			Pythagorean Theorem
     c^2 = 4^2 + 3^2			Replace a with 4 and b with 3.
     c^2 = 16 + 9			Evaluate 4^2 and 3^2.
     c^2 = 25			Add 16 and 9.
 = 			Take the square root of each side.
      c = 5			Simplify.

The length of the hypotenuse is 5 meters.

Example 2	Solve a Right Triangle
Find the length of the leg of the right triangle.

  c^2 = a^2 + b^2 		Pythagorean Theorem	
20^2 = a^2 + 12^2		Replace c with 20 and b with 12.
400 = a^2 + 144		Evaluate 20^2 and 12^2.
  400 – 144 = a^2 + 144 – 144	Subtract 144 from each side.
            256 = a^2		Simplify.
         = 		Take the square root of each side.
              16 = a		Simplify.

The length of the leg is 16 inches.

Example 3	Use the Pythagorean Theorem 
Multiple-Choice Test Item		Dave purchases a plot of land shaped like a right triangle.  The hypotenuse is 110 feet and one of the legs is 60 feet.  About how long is the other leg?
A.  50 feet	B.  7.2 feet	C.  92.2 feet	D.  41.3 feet

Read the Test Item
The three sides of the plot of land form a right triangle.  You know the lengths of the hypotenuse and one leg of the triangle.  You need to find the length of the other leg.

Solve the Test Item
Use the Pythagorean Theorem to find the length of the remaining leg of the plot of land.

		c^2 = a^2 + b^2			Pythagorean Theorem
	       110^2 = 60^2 + b^2			Replace c with 110 and a with 60.
	    12100 = 3600 + b^2			Evaluate 110^2 and 60^2.
    12100 – 3600 = 3600 + b^2 – 3600		Subtract 3600 from each side.
	      8500 = b^2				Simplify.
	   =  			Take the square root of each side.
	       92.2 ≈ b				Round to the nearest tenth.

The missing measurement is about 92.2 feet.  The answer is C.

Example 4	Identify a Right Triangle
The measures of three sides of a triangle are given.  Determine whether each triangle is a right triangle.
a.  10 cm, 14 cm, 18 cm			
     c^2 	= a^2 + b^2 			Pythagorean Theorem
  18^2	 10^2 + 14^2			Replace c with 18, a with 10, and b with 14.		   
  324  100 + 196			Evaluate 18^2, 10^2, and 14^2.
  324 ≠ 296			Simplify.				   
The triangle is not a right triangle.	

b.  15 in., 20 in., 25 in. 

     c^2 = a^2 + b^2			Pythagorean Theorem
   25^2  15^2 + 20^2			Replace c with 25, a with 15, and b with 12.	
  625  225 + 400			Evaluate 25^2, 15^2, and 20^2.
  625 = 625			Simplify.
The triangle is a right triangle.