3.2 Pythagorean Theorem & Missing Values

3.2 Pythagorean Theorem

Before we start

• You should know how to identify the sides of a right triangle

• The two sides that connect to make the right angle are the legs

• The side opposite the right angle is the hypotenuse, which is also the longest side

Multiple Choice

Which side is missing?

• a leg

• the hypotenuse

Multiple Choice

Which side is missing?

• a leg

• the hypotenuse

Multiple Choice

Which side is missing?

• a leg

• the hypotenuse

Multiple Choice

Which side is missing?

• a leg

• the hypotenuse

Multiple Choice

Which side is missing?

• a leg

• the hypotenuse

Multiple Choice

Which side is missing?

• a leg

• the hypotenuse

Using Pythagorean Theorem to Find a Missing Leg

• Here we have

   $a^2+5.6^2=10.6^2$  

• Simplified, that is  $a^{2\ }+31.36=112.36$  

• Subtract 31.36 from both sides to get  $a^2$  alone. We now have  $a^{2\ }=81$  

• We need to  $\sqrt{a^2}=\sqrt{81}$  to find the value of our missing leg

• The value of our missing leg is 9 in.

Using the Pythagorean Theorem to find the missing hypotenuse

• Here we have

   $21^2+20^2=c^2$  

• Simplified, that is  $441+400=c^2$  then  $841=c^2$  

• We need to find the square root of 841 because we want to find the value of c not  $c^2$  

• We now have to  $\sqrt{841}=\sqrt{c^2}$   

•  $\sqrt{841}=29$  ; the value of our hypotenuse is 29 km

Questions?