Lesson 7-7

For Example 2   Find the Length of the Hypotenuse
a. Use the Pythagorean Theorem to find the length of the hypotenuse. 

c

60 ft

80 ft

   			Pythagorean Theorem
   			Replace a with 60 and b with 80.
   		Evaluate 602 and 802.
   			Add 3,600 and 6,400.
     			Definition of square root
     c 	= 100 or –100		Simplify.

The equation has two solutions, 100 and –100. However, the length of a side must be positive. So, the hypotenuse is 100 feet long.

For Example 3   Find the Missing Length

b. Use the Pythagorean Theorem to find the missing length. 

15 in.

a

11 in.

                   		Pythagorean Theorem
                 		Replace c with 15 and b with 11.
                 		Evaluate 152 and 112.
        	Subtract 121 from each side.
         	     			Simplify.
           			Definition of square root
			Use a calculator.

The length of the other leg is about 10.2 inches.

For Example 5    Identify a Right Triangle
c. Determine if a triangle with sides of 30 inches, 16 inches, and 34 inches is a right triangle. Use the converse of the Pythagorean Theorem.

      c2 = a2 + b2		Pythagorean Theorem
    342  162 + 302		c = 34, a = 16, b = 30
1,156  256 + 900		Evaluate 342, 162, and 302.
1,156 = 1,156  		Simplify.

The triangle is a right triangle.