How to Solve Pythagoras Theorem Questions

Step-by-Step Guide

1. 1

   Step 1: Find the right

   Because this theorem only applies to right triangles, you need to determine which angle is the right angle.
   
   If the triangle does not have a right angle, you cannot use the theorem.
   
   Usually the right angle is denoted by a small box.
2. 2

   Step 2: or 90-degree

   The hypotenuse is the longest side of a right triangle, and will be opposite the right angle., The formula is a2+b2=c2{\displaystyle a^{2}+b^{2}=c^{2}}, where c{\displaystyle c} is the length of the hypotenuse, and a{\displaystyle a} and b{\displaystyle b} are the lengths of the other sides of the triangle., Remember, these are represented by the variables a{\displaystyle a} and b{\displaystyle b}.
   
   For example, if the triangle has side lengths of 3 and 4 cm, your formula will look like this: 32+42=c2{\displaystyle 3^{2}+4^{2}=c^{2}}. , Plug these new values into the formula.
   
   For example:32+42=c2{\displaystyle 3^{2}+4^{2}=c^{2}}9+16=c2{\displaystyle 9+16=c^{2}} , This sum is equal to the length of the hypotenuse squared (c2{\displaystyle c^{2}}).
   
   For example:9+16=c2{\displaystyle 9+16=c^{2}}25=c2{\displaystyle 25=c^{2}} , This will give you the length of your hypotenuse.
   
   For example:25=c2{\displaystyle 25=c^{2}}25=c2{\displaystyle {\sqrt {25}}={\sqrt {c^{2}}}}5=c{\displaystyle 5=c} So, the length of a hypotenuse of a triangle with side lengths of 3 and 4 cm is 5 cm. , If you know the hypotenuse and one side of the triangle, you can still use the theorem by substituting for the appropriate values.
   
   For example, if you know a right triangle has a hypotenuse measuring 5 cm in length, and one side measuring 3 cm in length, your formula will look like this: a2+32=52{\displaystyle a^{2}+3^{2}=5^{2}}.
   
   You would then solve the equation for a{\displaystyle a} instead of c{\displaystyle c}:a2+32=52{\displaystyle a^{2}+3^{2}=5^{2}}a2+9=25{\displaystyle a^{2}+9=25}a2=16{\displaystyle a^{2}=16}a2=16{\displaystyle {\sqrt {a^{2}}}={\sqrt {16}}}a=4{\displaystyle a=4}
3. 3

   Step 3: angle.

4. 4

   Step 4: Determine that the missing length is the hypotenuse.

5. 5

   Step 5: Write the formula for Pythagoras’s Theorem.

6. 6

   Step 6: Plug the value of the side lengths into the theorem.

7. 7

   Step 7: Square the length of the sides.

8. 8

   Step 8: Add the squared length of the sides.

9. 9

   Step 9: Find the square root of both sides of the equation.

10. 10

    Step 10: Use the theorem to find the sides of triangles.

Detailed Guide

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