Pythagoras’ Theorem

GEOMETRY

To be quite honest… I found this topic a piece of cake. I adore angles, and geometry because if you know the right equations, then you can defeat any nasty little question in a second.

So… you tight on Pythagoras’ Theorem? Well not to worry! All you need to remember is this rule…

a2+b2=c2 <- easy right? That’s IT. And when you get a nasty question like this one with angles:

You have to remember:

  • The longer side of the triangle (in this case 6.2m) is called the hypotenuse <- long word isn’t it? 😀 And the two shorter sides you can label as ‘a2’ and ‘b2’… you have the liberty to choose which one to name which. Got it?

<- This one’s a hard question to answer so I’ll give you an easier one if you’re a beginner.

 

Ok… so let me guide you through the baby-steps. There’s no rush, because if you do, you’re going to exit this blog having no clue of what I’m talking about.

  1. You have to find ‘x’. ‘x’ is known here as the hypotenuse (you could label it as ‘h’ or ‘c’) and you have to remember this: Always and I mean always ‘c’ has to be labelled on the hypotenuse. Got it?
  2. Remember the rule/equation? a2+b2=c2? <- that is extremely important to remember so read well. I am going to label ‘a’ ‘4cm’ and ‘b’ ‘3cm’, ok? So what do I have to do? Use your brain cells for this one… Because it says in the equation ‘a2’, this means that the ‘4cm’ is going to converted into ’16’ because when squaring these numbers you need to ‘4 x 4 = 16’… understand?
  3. Moving on to ‘b’ which is ‘3cm’ you need to square it as well so you can have the same units. So this makes ‘3 x 3 = 9′. Got it? So now we have on one side ’16cm’ and on the other ‘9cm’ but we still don’t know about ‘x’. So what do we do next?
  4. Following the rule of: a2 + b2=c2… 16 + 9 = 25. So now you know the answer of ‘x’ but you haven’t finished yet so don’t get too happy.
  5. You need to square root 25 to get it back to it’s original unit and that would be 5cm. You square root 16 back to 4 and 9 back to 3 and there you go!
  6. This makes ‘x’ or in this case the hypotenuse or ‘c’ ‘5cm’. That’s your answer!

Now, If you want to take this one step further then carry on reading.

REMEMBER THE RULE: a2 + b2 = c2 <- (and I’m going to keep bragging you about this until it’s tattooed on your brain!)

This Question as you can see, the hypotenuse (‘c’ or ‘h’) is already labelled but what about ‘x’?

So do the method in your head but you instead work your way backwards.

  1. a2 + b2 = c2 <- right? I’m going to label ‘4.9cm’ ‘a’ and ‘6.2cm’ ‘c’ (‘C’ IS ALWAYS LABELLED THE LONGER SIDE). Do the same into squaring ‘4.9cm’ to be alike to ‘a2’ so that will make it ‘24.01cm’ Square ‘c’ which is ‘6.2 x 6.2 = 38.44cm’. Now… this is the part where it might get confusing.
  2. Take ‘c’ which is ‘38.44cm’ and subtract ‘24.01cm’ from ‘c’ and you’ll get ‘b’ (x) which equals ‘14.43cm’.
  3. Square root the answer to make it the same units as the others and that will lead you to the answer which is…. dun dun daaahhhh… erm… wait… let me work it out… which is: 3.79868398264452. Round it up to one d.p (decimal place) and CONGRATULATIONS. YOU HAVE THE ANSWER.

Practice these two methods all the time until you get the hang of it because I guarantee you will have it in your exam paper.

 

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